Paul explains himself quite well as to why he and his organization (of which I am a member) aren't in the animal rights movement as he describes in the below paragraph. It can't be any clearer than this. He's not against animal rights, he just doesn't like his organization being labelled as an animal rights enforcer and being mixed in with groups like Greenpeace and the World Wildlfe Fund that just exploit the gullible public to donate vast amounts of money to their 'animal rights movement' but do nothing with it. This is what he means:

"Now first of all I don't see being accused of as an animal rights
organization to be an insult. PETA was co-founded by one of my
crew-members and many of my volunteers come from the animal rights movement. But
it is not accurate to refer to Sea Shepherd as animal rights when our
organization pushes a strict conservation enforcement policy."