Do I hate PETA? No, not really. I can't hate them, they're too fuzzy! Anyway...
1. One issue I have with them is the fanboy(girl)ism they attract. They attract a type of member that is in it for the "feel good" factor. These people have this warm, fuzzy feeling in the pit of their stomach when they think they're helping the poor animals. Yes, there's plenty of animals that need help, and the basis of their group is a good cause, but when you recruit mindless zombies of propoganda spewing zealots (kinda like religion 0_o) to hand out your propoganda, they're going to draw down some hate. Yes I realize this is rampant amongst many organizations, but that doesn't make it any less annoying for me.
2. The extremism just gets under my nipples. The destruction of private property irritates the crap out of me. I don't care how much money the individuals have or how much attention their going to get. It is wrong; end of story. You do not destroy other people's things. It is as much of a crime as the things they're trying to stop.
3. The insulin argument is actually a good one that you seem to play off with out giving any thought. My mother is type 1 diabetic. Here's some information on insulin in general as well as the current synthesis methods.
http://en.wikipedia.org/wiki/Insulin
http://en.wikipedia.org/wiki/Recombinant_DNA#Synthetic_insulin_production_using_DNA
Oh my goodness! The poor bacteria plasmids! How could we not realize that they're using these horrible farms of bacteria to create insulin!? :cough: (tongue in cheek there) Many medical advances were first tested on animals to fine tune them for human consumption, if not derived directly from animals to begin with. If the members of PETA are so quick to demand a stop to animal testing, why not go straight to human testing? I have an idea! They can submit themselves first! That's how they can stop animal testing! :cough: Nature itself uses it's own genetic testing day to day. Natural selection anyone? The animal that has the best genetic code for it's environment is determined to be the dominant one. As far as I'm concerned, we're just helping it along. =P Which leads to my next point.
4. If they're really concerned about humans meddling with the lives of animals for their detriment, then they really need to round up every domesticated breed in existance and destroy them as soon as possible. We have bred so many genetic deformities, especially into dogs, that it's sickening. So many breeds have a high tendency to cancer, have faulty joints and have basic psychological disorders that are inherent to individual breeds. Round them all up, disallow anyone to have any more pets, since holding them against their will is evil, and destroy them to purify their genes. Only allow the wild specimines of each family (wolves, coyotes, foxes, dingos, etc...) to exist. Why not? Don't these genetic deformities cause suffering amongst the populations? Uh huh...
Conclusion (tl;dr) - PETA started with fantastic ideals. Their beginnings were in well founded logic with a hope to help living things that couldn't fight for themselves. They've lost that and turned into a group of shock inducing extremists who turn less people towards their way of thinking then they have against it. Many PETA supporters do so for the "feel good" aspect, instead of a true conviction for their beliefs. They are hypocritical on many things, such as using medications that were derived from animal testing. If they were so convicted in their beliefs, they would boycott these things. So no, I don't hate PETA, but I far from love them. There are many alternatives to what they do, such as leaving the damn pets with their loving families. My family and I love our dog damnit, and we personify her to an unhealthy degree. Let us enjoy her company and she enjoy ours. I can guarantee you, she doesn't know any better when she gets pat on the belly or gets a biscuit.