Why people are so against lich pcs?
You can do whatever you like in your game. In my experience it may be fun in the short run, but tends towards the disruptive in the long run. Players looking to play monsters are typically just looking for a quick power boost, making them the center of action/attention of the party. As for allowing a lich to remain under player control - I assume the lich (which seeks power and extending its unlife above all else) is immediately abandoning his party to continue his lichly pursuits, right? No? Why not? Continuing to adventure with a party of humanoids doesn't sound very lich-like, does it? Why aren't there hordes of lich-adventurers in the world? Why is a non-evil party content to tag along with a powerful evil undead being instead of destroying it? These are things to consider. If you can answer all of them them to your satisfaction, then great. Often I've found DM's allowing monster player characters haven't thought much beyond "The player thought it would be cool".
I fully agree with the section "The monster as a player character" from the 1st Edition DMG (page 21):
"...As to other sorts of monsters as player characters, you as DM must decide
in light of your aims and the style of your campaign. The considered
opinion of this writer is that such characters are not beneficial to the game
and should be excluded. Note that exclusion is best handled by restriction
and not by refusal. Enumeration of the limits and drawbacks which are
attendant upon the monster character will always be sufficient to steer the
intelligent player away from the monster approach, for in most cases it
was only thought of as a likely manner of game domination. The truly ex-
perimental-type player might be allowed to play such a monster character
for a time so as to satisfy curiosity, and it can then be moved to non-player
status and still be an interesting part of the campaign -and the player is
most likely to desire to drop the monster character once he or she has
examined its potential and played that role for a time. The less intelligent
players who demand to play monster characters regardless of obvious con-
sequences will soon remove themselves from play in any event, for their
own ineptness will serve to have players or monsters or traps finish them off.
So you are virtually on your own with regard to monsters as player
characters. You have advice as to why they are not featured, why no
details of monster character classes are given herein. The rest is up to you,
for when all is said and done, it is your world, and your players must live in
it with their characters. Be good to yourself as well as them, and everyone
concerned will benefit from a well-conceived, well-ordered, fairly-judged
campaign built upon the best of imaginative and creative thinking."