First: PETA. I don't know anyone who doesn't think PETA is a gigantic (unfunny) joke. I'ved lived with vegetarians, vegans, and animal welfare advocates and I have yet to see a single one who doesn't think that PETA is a ridiculous waste of time and money. Instead of dealing with actually pressing issues, they just try to get involved with anything new and popular, no matter how minor, to spread brand recognition. This is presumably to increase awareness of larger issues, but you'd think by now they'd realize that it doesn't really work when they're advertising outrage over such stupid things.
Second: Really? A rat in a ventilation duct? REALLY? I mean yes, I can see why PETA would be against this, but they must have more pressing issues to deal with. On the scale of things to be concerned with regarding animal safety this is like a negative ten. What next PETA, press releases about a movie where someone swatted a fly? There are so many much bigger problems to deal with and it blows my mind that they're wasting time on something like this (this is why no one takes them seriously).
Third: They're acting as though there wasn't a reason to kill it. He was trying to silently creep through some vents and was being bitten. That can interfere with you ability to sneak past a bunch of people with guns who want to kill you. Whether you think the killing is justified by this is one issue, but acting as though he just killed it for no reason is dumb.
Four: The inevitable problem with PETA and other groups' criticisms of animal violence in popular media: this is a game about mowing down groups of humans. I guess you can point out that the humans have involved themselves in this whereas the animals are mostly innocent bystanders, but if you're concerned about violence (especially if you're going to play the "this is where kids get violent ideas" card), shouldn't you maybe mention the people being killed somewhere?
Five: Now video games aren't just teaching kids to murder each other, they're also teaching kids to murder animals.
(To be fair, I did pause at the rat killing and it did seem sort of superfluous - it was sort of gross and added more or less nothing to the game.)