Professor X, team founder and Big Good has many counterparts among the villains faced by the X-Men.
Magneto. Both are influential and outspoken men campaigning for Mutant rights and they worked together in the past helping Mutants and Jews who survived Nazi Death Camps, even uniting together against Wolfgang von Strucker and HYDRA. However, Magneto and Xavier differ when it comes to their perspective on the world, Charles sees the good in all humanity and dreams of "Mutantkind" to be one with them. Magneto however came to different a conclusion after spending his childhood in Auschwitz, he saw mankind as repugnant and unredeemable and considers Mutantkind to be superior to humans. Both the Professor and Magneto deeply care for their respective groups but while Xaiver's occasional leniency causes trouble for the X-Men, Magneto's megalomania has ensured the loss of his brotherhood and his mutant utopias multiple times. When Professor and Magneto's consciousness fuse together they become the Invincible Villain Onslaught signifying just how goddamn unstoppable both men would be if they ever truly worked as one.
Cain Marko aka The Juggernaut, Charles's stepbrother and his fierce enemy. Both men are two of the most powerful individuals on the planet but Marko's strength is physical, while Charles is a powerful psychic. Xavier can't move without his wheelchair while Juggernaut's mobility cannot be stopped. Both Xavier and Marko suffered under the hands of Cain's father Kurt Marko but Cain deludes himself into thinking Charles was favored by his own father which makes Cain hate Charles even more despite Charles repeatedly telling his adoptive brother that he was abused as well. Marko gains his powers from the Gem Of Cyttorak, although Cyttorak actually wanted Xavier to be the Juggernaut. In X-Men (2019), Xavier and Juggernaut end up with Swapped Roles, while Charles becomes the Ambiguously Evil leader of Krakoa and possesses Mutant supremacy overtones, Cain turns over a new leaf helping Damage Control and using his immense strength to protect the innocent. It's even reflected in the inital reunion between the stepbrothers as Cain is the invalid and Charles is the powerful one wearing the scary domed Cool Helmet, except Charles does it make clear that he still cares for his stepbrother greatly.
Cassandra Nova Xavier, the Professor's Evil Twin sister. Cassandra is an evil "anti-self" entity literally created to balance the good that was Xavier with pure evil, so evil in fact little baby Charles tried to kill his sister inside the womb before she could be born. Years later Cassandra comes back for revenge and shows the X-Men just how unstoppable an evil Xavier would be as she takes over her brother and creates absolute havoc. It takes the combined psychic efforts of Xavier, Jean Grey and Emma Frost just to stop her... briefly.
Emma Frost, the telepathic headmistress of her own school, recruiting and training young mutant students.
After her true descent into darkness, Moira MacTaggert becomes an Evil Counterpart to Charles even taking up the moniker "Moria X".
Although Mystique lacks any of Wolverine's powers, they've both lived over a century and were a mutant Bonnie and Clyde for multiple years. Both Wolverine and Mystique have had numerous illegitimate children, are prone to selfish desires and are loners. However, Wolverine even at his very worst has a moral compass which Mystique simply lacks. Logan knows deep down he's really not that different from Mystique, which pisses him off when she can correctly call him a Hypocrite when he tries to act holier than she is. Still at the end of the day, Wolverine for all his faults has friends while Mystique doesn't and she suffers greatly for it.
Magneto, the usual Big Bad for X-Men stories, has a pair of Good Counterparts.
Lorna Dane aka Polaris, Magneto's daughter. She has her own magnetic powers and is the embodiment of what Magneto would be if he did genuinely use his powers as a source for good as Lorna does for the X-Men and X-Force. It helps that Polaris has very few of the Anti-Human hangups that her father has in full. Though Polaris can slip into her father's extreme ways Depending on the Writer.
Kitty Pryde. Like Magneto Kitty suffered stimga and racism for being Jewish, though Kitty overcame her trauma and strove to make herself a better person who helps others, while Magneto had the opposite reaction, desiring to destroy all who subjugate others all while becoming a subjugating tyrant himself. In fact, Magneto once nearly killed Kitty, causing him to instantly realize what a goddamn Hypocrite he was being and surrender to the X-Men immediately. Kitty even becomes The Leader of the X-Men and Magneto turns evil again making their connection all the more apparent as the opposing Big Good and Big Bad.
For Jean Grey:
Emma Frost, both being the beautiful psychics for their teams, the Hellfire Club and X-Men respectively. Their telepathic power is so great that when Jean and Emma first clashed it caused shockwaves. However, Jean is affectionate and kind while Emma is a Ice Queen being very haughty and often cruel. Although Emma makes a Heel–Face Turn and joins the X-Men, their counterpart status is still emphasized, as Emma ends up dating Jean's husband Scott Summers, and Emma is still the more ruthless of the two. In Avengers vs. X-Men, Emma is taken over by the Phoenix Force and becomes just as evil as Jean was when she got possessed.
Madelyne Pryor is Jean's literal Evil Knock Off created by Mr Sinister to woo Scott. Madelyne possesses all of Jean's abilities and is even a potential host for the Phoenix Force which is why Mr Sinister cloned her a few dozen times. Madelyne is also a chilling reminder of what Jean could be without her loved ones, the X-Men, as Madelyne becomes a Broken Bird when Cyclops abandons her and becomes the Goblin Queen. Jean legitimately cares for her evil clone and is distraught when she has to bring Madelyne down.
For Scott Summers/Cyclops:
Alex Summers/Havok originally was the evil counterpart to his brother, having similar energy beam powers, but he later makes a Heel–Face Turn.
Scott's other brother Gabriel Summers aka Vulcan, who was ripped out of their mother's womb by aliens, came back to Earth, was seemingly killed by a living island, and then came back again as a proper villain. Gabriel is likely what Cyclops and Havok would have become if their mother didn't push them safely out of the plane as kids.
Callisto to Storm. Both are formerly homeless women who have a lot of skill with knives and who found themselves being worshipped, Storm by the Kilimanjaro Tribe's men and Callisto by the Morlocks. Upon meeting her Storm can understand Callisto's actions better than her fellow X-Men as Colossus is confused when Callisto is seemly in love with Angel but Storm corrects him knowing it's more desire and reflects own her own Dark and Troubled Past. The similarities get bigger as Storm leads the Morlocks as effectively as Callisto did and later in M-Day she joins Storm in protecting the Runaways, showing when it comes to the downtrodden she and the "weather witch" are not that different. In modern comics, they consider each worthy opponents as at one point after Storm catches the butterfly knife Callisto throws at her face, they hug.
To Gambit:
New Sun is Gambit's evil Alternate Self and counterpart. He who comes from a Earth where Gambit didn't fix the Power Incontinence he had with his Having a Blast powers by having it surgically removed from his brain by Mr Sinister and as result scorched the earth. New Sun travels to different Earths killing every single version of Gambit he can find before being stopped by Earth-616 Gambit, who has his own powers dialed up to match New Sun. Gambit isn't stressed about his antithesis, only lamenting that New Sun doesn't have his "sexy" accent.
Fantomex. Both are trench coat wearing highly skilled Mutant thieves with assassin training who, despite lacking a truly powerful Mutation, are still incredibly dangerous.They both have a French accent although Fantomex only does it to annoy people. When Storm orders Gambit to take down Fantomex, Gambit is very grateful for the opportunity, finding it cathartic.
Mystique represents what her two children Rogue and Nightcrawler could become if they didn't gain/have a moral compass. Rogue, like Mystique, has the ability to steal entire lives from other people and both women feel particularly alienated by society, though ironically Rogue's Power Parasite abilities allow her to feel emotions of other people she becomes a selfless person because of it, while being an Involuntary Shape Shifter ironically makes Mystique extremely selfish, introverted and apathetic. Nightcrawler, whom Mystique actually gave birth to, signifies what she could be if she wasn't so jaded against society, since Nightcrawler takes pride in his appearance while his mother Mystique is actually ashamed of her natural mutant form.
Speaking of Nightcrawler, his Big Red Devil father Azazel is also a evil counterpart for him. Being catholic Nightcrawler is naturally disposed to his satanic father but their powers are connect them and both father and son invoke the Swashbuckler ideals. Also a group of Demon Bamfs created by Azazel branch off when Nightcrawler tames them creating more counterparts◊.
Daken to X-23. Both are the children of Wolverine, but Laura takes after her dad as an Anti-Hero while Daken is a villain.
Deathbird of the Shi'ar Empire is the evil counterpart of her younger sister Lilandra (Xavier’s Love Interest) as whereas Lilandra is caring and heroic, Deathbird is a colossal bitch.
While they never cross paths, the Blink of Age of Apocalypse gains one briefly in her own Earth-616 counterpart, who despite originally being created as a Sacrificial Lamb for the set-up of Generation X, was revealed to have actually survived, and was found and manipulated by Selene before being freed from her control.
Ebon Samurai is the Good Counterpart of Wolverine's enemy Silver Samurai. Word of God states that Ebon Samurai was a police officer that was killed by Silver Samurai, only to be resurrected as a vengeance-driven superhero.
Stryfe is the Evil Twin of Cable and therefore his evil counterpart. While Cable is The Stoic doing what he needs to do protect the future and his loved ones at any cost, Stryfe wants absolute dominance in the Bad Future, and unlike his good twin his Time Travel exploits are done with his bloodthristy desire for power in mind. Stryfe also represents what Cable would have become if he'd fallen under the heel of Apocalypse: an unstoppable amoral killing machine. Stryfe embraces his cybernetics while Cable struggles with them every day.
Powers of X reveals this is part of Moira MacTaggert's Mutation as thanks to Reincarnation she has lived multiple lives, making her an Evil Counterpart to herself. While Moria is still a good person in most of them, in her third life she created a cure for Mutantkind and tried force it upon them before Mystique had her killed, in her eighth life Moira joins Magneto and tries to conquer America with him before they are stopped by X-Men and Avengers. Worse still in her ninth life Moira joins Apocalypse slughtering Xavier, Magneto and almost everyone else, but she also awakens Nimrod an unstopple super Sentinel and is later killed by Wolverine albeit willingly. However in her tenth life Moria having to knowledge of all her previous lives, is able to pass on it on to Charles Xavier thus help him safeguard the future... until it's revealed she was Evil All Along.
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