Sometimes I quit games because of the match connection. Like playing Destiny the other day I could see my opponents were from Brazil (they had stuff like BR in their title) and they were lagging all over the shop. I quit that game pretty quick.
In other instances, I've left games because of scenarios I felt were unfair. For instance I was playing D2 comp with a friend, plus a random, against a team of three. We lost pretty badly, but we stuck it out. I match again and it puts us against the same players, no problem, take the loss and match again. This time it's clear that our random team mate has over 50% of our teams total deaths, so he's tanking our score. Next up, the same 3 players, the same rando on our team, no thank you. I quit out as soon as the match started.
Sometimes I've quit out because of harassment. I remember playing battle born with some guys before and they were being jerks, blaming me for something (even though, if I recall I was the only one doing okay on our team at the time). It just came down to them being a group of friends and me being solo, so they were looking for someone to blame. Anyway, they were very rude on the mic so I just told them 'good luck 1 man down, that'll help turn this game around' and quit.
In rare instances I'll leave just because I'm not having any fun. In those instances I don't mind that I'm being beaten or whatever's happening in the game, but I just find the mechanics of the game frustrating. For instance getting spawn killed over and over in Destiny 2, or getting repeatedly killed by killstreaks in a Call of Duty game.
I probably quit out of a match (for one of these various reasons) around once per week.