The reasons behind the taboo of male genitalia, despite the fact that half of the world's population has it, are multiple. While the Ancient Greeks seemed to have no problems with it and nudity was even a common practice for men in the Olympic Games, male nudity, or any nudity really, didn't sit well afterwards. In Ancient Rome already, only male slaves (and female slaves as well) would walk around in the nude as a mark of their servitude and low social rank, which is an element of the Shameful Strip trope.
Since then, many of the world's major religions required some level of modesty. To show one's genitalia in public is considered at best immodest and at worst sinful. This is no doubt because genitals are sexual organs and most religions teach that sex is a private matter that must not be discussed publicly. Of course, simply having genitalia is not inherently sexual but this basic biological fact tends to get overlooked when it comes to discussions of what constitutes immodesty.
It's also important to note that, unlike the vagina which needs to be seen up-close and "open" to be considered obscene, the penis is much harder to hide from sight on a naked man seen frontally, even from afar, which parallels the logic behind Nipple and Dimed.
Additionally, as noted on the main page, most writers have historically been male (as well as straight) and therefore have little interest in depicting something that they view as just another body part. That is, unless Naked People Are Funny is thrown into the mix, in which case the penis is often used as a gag and a fleeting one at that. This is not to say that most media in which penises are seen are written by straight women and gay men. Rather, as the examples on the main page show, the penis is rarely depicted as an object of sexual desire outside of pornography.
Finally, it may simply be that when one is shown a penis, one cannot help but think of sexual activity. Most media depict the penis in its natural state i.e. limp. But it is all too easy to imagine it as erect and that automatically carries with it a sexual connotation. Thus, it must be kept out of sight because the human imagination cannot help itself when it comes to sexual matters.
No matter what, a visible penis is always perceived as obscene, or at least immodest. There are some exceptions to this rule of course. When a man is dead on a forensic's table is the most common one, mostly because a dead man's penis can no longer be used for sex. Anatomical depictions of the human body also count since the dry scientific surroundings of such pictures completely dispel sexual aspects thereof.
