While Gygax spoke against this, he also allowed it in his own games and in fact, in 1e, there are some hidden guidelines to support it. Deities and Demigods gives us rules for calculating hit points for non-humans with levels, and the Dungeon Masters Guide notes for the reincarnation spell offers a little bit of advice. I don't know to what degree these notes survived into 2e.
Gygax's dislike of this as a "normal" option was that he saw it as characteristic of a style of play where bonuses were never balanced by logical and consistent penalties - the monster PC is expected to be all "up-side". The classic example being the drow: play one if you like, but be prepared to be hunted down and persecuted by every intelligent surface-dweller, and many underground ones too. If the DM is running their world fairly, non-evil drow have a short life expectancy. In fact, many DMs indulge such players to the point where it makes no sense to play anything else, at which point the entire humanocentic PoV of the campaign collapses.
He seems to have believed that players who persistently want to play a monster are simply incapable of seeing that the game is about progression and growth; playing a monster is really a sly way to get a load of up-front bonuses. My experience is that this is true, but I also agree with him that it can be fun occasionally and I have fond memories of my lizardman cleric, although he snuffed it at 3rd level.