I'm designing some custom races for my campaign and I'd like to allow large size characters. It seems that large characters are discouraged for some reason and although I'd like to know why what's more important is finding some official rules or guidelines on how to create large character races like minotaurs, half-ogres, centaurs, etc.
There are guidelines for creating playable races in page 285 of the DMG, however, it doesn't go into detail on creating Large races, specifically (nor do they really go into detail on making medium characters, mechanically, save for the 'compare to other already-established races' approach). This is largely because playable races are only sized between Small and Medium (4 to 8 feet tall).
Take a look at the Goliath in the Temple of Elemental Evil player's companion, the Minotaur and Centaur race in their Unearthed Arcana version, and the final version of Minotaurs and Centaur in Guildmasters' Guide to Ravnica, all these races sound like they should be Large. In fact, if you take a look at page 223 of the Monster Manual, you'll find that Minotaurs are Large creatures, despite this, playable minotaurs are Medium. Of course, you could argue that the Krynn minotaurs who don't dwell mazes have evolved to be smaller. Then again, who's to say it wasn't a design constraint? ;)
So, why aren't there Large player-characters?
Weapon damage dice
In page 278 of the DMG, you can see rules on damage dice of creatures. A Large creature is going to wield oversized weapons, this means their damage dice are doubled, tripled for Huge, and quadrupled for Gigantic. A Large PC with a Glaive will be dealing 2d10+str, almost doubling the damage output just by being large, at 1st-level.
A Large creature occupies a 10x10 ft area, making it more of a threat in battle especially when it comes to blocking and generally being a 'presence' in any encounter.
As mentioned in this tweet by @ThinkingDM, auras emanating from Large PCs cover more squares than Medium PCs. Specifically, for a 5' aura, Large PCs cover 12 squares versus the Medium's 8 squares. In 10' auras, Large PCs cover 32 squares versus the 24 from Medium.
In order to accompany any typical adventuring party, a Large PC will need to squeeze in most places a typical adventuring party would visit. Whether it's a tavern, a forest gnome's tree house, or a mine tunnel made for dwarven miners, a Large PC will be continuously at a disadvantage while squeezing through most other terrain a Medium creature would have no problem fitting in.
These traits, inherent in the creature's size alone, make a Large creature fairly overpowered in most any game.