I think it's a combination of just something that rubs a player the wrong way, combined with the fact you're almost forced to stick with them or you lose an entire character slot. If I don't like say, Imoen in Baldur's Gate, I can tell her to take a hike and replace her with someone else. In DA or ME you're kind of stuck, even more so in DA2 where you can't tell them to get lost until the game wants you to be able to.
You don't like "Anders" and think he's nowhere near the character he was? Tough luck, you're saddled with him until at least Act 2.
ME3's especially grating, because you're supposed to let a character who's actively distrusted you - Ash or Kaidan - and thrown it in your face time and time again just waltz back onto your team instead of any number of people who actually believe in Shepard. If you do tell them to walk, you just lose a character slot.
But at least in ME 3 you are not forced to take Ash/Kaidan, I never did.
Anders was a unique case, but it is understandable because you don't know how much of a whining hypocrite he is.
I really liked DA:O approach to Companion System, If you didn't like someone you could tell them to take a hike.
As for hating Companions as soon as you meet them, well it doesn't matter, because you would start metagaming when recruiting companions, for eg : If there is an insane Companion in DA:I (god I hope not) you would not dismiss them outright like most 'Real' people would, because you know the game will give you 9 permanent companions, so this insane companion would not slit your throat in your sleep, and with enough positive influence you would be able to befriend them.