What is wrong with comparing people to animals?
Because throughout history it has been a justification for oppression, slavery, war, and extermination. It is a way to "other" fellow human beings and distance people from them.
Things like the Washington D.C. billboard comparing slavery to animal rights is essentially comparing african-americans to livestock, which is the very same logic that had white americans enslaving them in the first place. They're actually diminishing the crime of slavery by comparing it to something most people find completely acceptable. It's also appropriating a not-so-distant past to justify your own completely unrelated goals. Which all works to overshadow the fact that the legacy of slavery is very much with us, and racism is still very much a problem.
Think really carefully about which people PETA chooses to compare to animals. Are they EVER white males? Ever? Or are they only highly sexualized women and various minority groups? I guess they want to imply that animals are another persecuted minority group with this comparison, and as a result they're putting for example the jewish community on the same level as cows or sheep. And diminishing the Holocaust by suggesting it's only as bad as what you can find at your local McDonalds.
If you have to ask whether racism and sexism and outright genocide are worse than, say, eating a hamburger, your priorities are waaaaaaay out of wack. And that's exactly what groups like PETA do - they skew your thinking until the way your fellow human beings are treated is less important than your holy cause, and absolutely anything is acceptable if it advances your goals.