It can be for any reason. You like the type strengths, the pokemon that have that type, the power of utility of the moves, any reason.
I apologize in advance for the tirade on Grass.
Fav Attack type: Ground. Earthquake is my all-time favorite move. It's SE against 5 types, being one of Poison's only weaknesses, Electricity's only weakness, and Steel, which resists 12 types. It's only not effective against Grass and Bug, both of which are easy to work around, and Flying is of course immune.
Least Fav Attack: Grass. It's always been worse in comparion to sister moves of other types. For example, Vine Whip and Mega Drain have much less PP than Ember, Thundershock, and Water Gun. Giga Drain is much weaker than Thunderbolt, Flamethrower, and Ice beam, and didn't exist in Gen I. Solarbeam was a two turn move as opposed to Fire Blast, Thunder, Blizzard, and Hyrdo Pump. Though to be fair, all the other 120 series moves had some kind of drawback: Fire Blast had low PP, Thunder had low accuracy, Blizzard had both, and Hydro Pump isn't available in TM form (maybe it was in Gen I, I don't remember). It shares advantages against Ground and Rock with Water, so you're better off with using Water for STAB, but most Water types have a Ice type move anyways, so it's risky. Finally, they have 5 weaknesses, most of which are quite common In-game.
Fav Poke type: Fighting. There's just so many that I like using: Blaziken, Lucario, Toxicroak, Conkeldurr, Hitmonlee, the list goes on. Also, Flying and Psychic moves aren't that common in competitve play (in a relative sense), so that's a plus.
Least Fav Poke: Bug. While there are of course some exceptions (Scizor and Heracross spring to mind), Most of them just aren't that good and carry an "early game" stigma with them. They don't have good stats, There aren't many good Bug-type moves, and they're almost always paired with Poison, Grass or Flying typing.
Favorite Attacking Type: Dragon. Resisted only by Steel. Sure it's only Super Effective against other Dragons, but when you consider that it hits 15 other types for neutral damage, and most Dragon Type moves have high Base Power, it's pretty amazing.
Least Favorite: Poison. It's only Super Effective against Grass Pokemon, which I don't see that much of anyway. And Toxic is overly trollish.
Favorite Type: Tie between Water and Dragon. Water was my favorite type when I started, Mudkip FTW. But now I'm a fan of Dragons for reasons listed above, and also because Salamence, Garchomp, Giratina-O, Hydreigon, Reshiram and White Kyurem.
Least Favorite Type: Poison, again as listed above.
PKMN Black FC: 2237 3659 0319 PKMN White 2 FC: 1120 8438 5851
^Yeah, Poison is one of, if not the worst attcking types, but it's actually a pretty decent defensive type. A 2:1 resistance to weakness ratio isn't bad, and a lot of Poison types have good Defense; that's like a trait of the type or something. This is me personally, but I actually like a lot of Poison types, even If I never use them. Ones like Wheezing, Venomoth, the Nido families, Ariados, Crobat, Sevipe, Toxcroak, and Scolipede. i like their designs and moves, but they're often not good enough to qualify for my main team.