A lot of the strange tests that Elminster is put through like making him live as a woman, be a thief, be a priest, being a mercenary, and so on are designed to teach him empathy. Which is a quality almost all other wizards on Faerun lack.
The one time Mystra freaks the fuck out with Elminster rather than handles him with a gentle but firm hand is when he stumbles over some of Karsus' research notes. Which makes sense as Karsus killed her previous incarnation of Mystryl. Worse, Elminster is one of the few mages in the Realms who could theoretically follow and understand Karsus' research in no small part to Mystra's education of him.
Elminster's hatred of Manshoon may just be their shared Archenemy status but it may also be due to the fact that the latter would remind the former of the Mage Lords that killed his family. Manshoon is the kind of arrogant magocrat that took over his homeland.
