I get annoyed when people refer to things as 'immersion breaking', without actually thinking about it first.
The worst incident of this I have seen was back in Nov 11 when Skyrim came out, and everyone jumped on the 'it's cool to hate Skyrim' bandwagon... or the 'It's not my kind of game anyway, so I will go out of my way to say why I don't like this installment'. And I saw a thread on here where someone listed all the ways Skyrim 'broke his immersion'.
One of these ways was the graphics. Aparrently they were really shit, and looked like a previous gen consoles efforts. And when pressed, the reason he gave was because when he ran point blank into a wall, the textures went slightly blurry/pixilated and aparrently this made it completely unrealistic and broke his 'immersion'.
We then had a spate of threads all about immersion, which luckily died off, but you still see the point used from time to time.
Now... the issue is the whole term 'immersion'. Immersion is how involved you feel with a game, and how much it sucks you into playing it, and getting into the story/characters/world. Games have had varying levels of immersion throughout the last few decades, with some doing it well and some not so well for a variety of reasons. The biggest reason is story. A gripping story, well thought out and with interesting characters... especially with a bit of flair (or 15 bits of flair minimum) will make a game particulary immersive, and you will overlook bad mechanics to keep playing.
Another way a game can be immersive is by giving you lots of rewards and goals, and keeping you intersted that way. This is seen the most in multiplayer games, where you are constantly working towards the next unlock, or device you can show off.
Things such as game mechanics, or bad character design, even bad voice acting, can detract from this immersion by contsantly pulling you out of your zone, and can overall ruin a games exerience for you. The problem with most people who use it as an arguement, is they use it to make themselves sound clever and like they know what they are talking about, even though the thing they are talking about is really trivial. The thing they don't actually see is that the real reason the immersion was broken is because they were not immersed in the gameplay and story to begin with, and this is not usually the games fault, but the fact that the person playing was expecting the game to fail, or were being over critical and only trying to fault it.
And that is my issue with that arguement...