I generally tend to look at human and animals rights on a fairly even playing field.
And while I do believe that animals need more rights in certain areas, there's a limit. I do not agree with PETA on any level that people should be vegetarian, it simply isn't part of our intended diet.
I would say if anything, the thing I find the most annoying is how arrogant humans tend to be how much they over value themselves over other creatures. I tend to look at most life in a similar manner, if I person dies I don't feel any more or less remorse than I would if it were a cat or cow or whatever. Life is life and I don't care who it is (unless it's obviously someone close to me. Which is obviously going to hurt, I can't change my emotions about that, nor should I.)
I also don't have an moral issues when it comes to food. I don't selectively pick certain species I find cute and generalize their lives as being important based on this. So, yeah, guess what, I'd eat a cat or a dog if it was available. I love pets, but the thing is, that cat on my plate is not my pet, nor does that entire species get special treatment because I like my pet. One thing I've always found rather amusing and intriguing about fictional vampires is that they put humans onto the food chain and give them a taste of what it's like to be just another animal. Also, in case anyone is wondering, I have no moral issues about people eating humans, if that were legal either. Granted, it's a tad bit strange since it would be cannibalism but I still don't have a problem with the concept of humans being a food source. (Obviously I don't want to be eaten by something, but I'm also not likely to legally oppose it in order to save my selfish ass.)
Some things I do find really disturbing about lack of animal rights is how screwed up the living conditions are for most animals bread for food, which really needs to be changed. As it is, I consider hunting for food in the wild to be far more humane by comparison. Sure, everyone likes to think about the big bad hunter shooting the cute wittle animal, but you know what? Those animals had a far better life than what you buy at the grocery store. Another thing I find disturbing is how if a person is accidentally killed, the police will mount an entire investigation into the entire thing and go to extreme lengths to punish whoever is responsible. An animal gets accidentally killed a simple "Oops" will suffice and everyone moves on, no investigation required.
There's loads of other things I could ramble about, but I think I'm going to cut it off here before I get into Wall of Text Land.