I think probably the term is a kick back against being labelled soft, or "spoiling' your child, or "making a rod" for yourself.
I think it's also pretty disingenuous to suggest that any other way is not bringing your child up with love and affection. Of course everyone is! To suggest someone following GF does NOT love their child is ridiculous and offensive.
But see - I would say that AP is just a part of one sum on a spectrum of ways of raising your child. Natural parenting, playful parenting, positive discipline...all parts of that sum that we personally naturally gravitate towards. Not doing sleep training, not implementing the "naughty step", not shouting at a naughty child or to an extreme extent...not smacking. Always going to them when they cry, even if it's for the billionth time that night. All these things encompass AP. It's not about not being able to BF - or choosing not to - and therefore you're not allowed to say you're AP.
I disagree about labels. We need descriptions, things we can say to communicate when we talk about things. Some people who practice AP are insufferably smug but I'd suggest that's them as individuals, not because they subscribe to attachment theory. I also happen to think people who are at the other end of the spectrum, people who say if you don't do sleep training, you're just not "prepared to put the hard parenting work in" are also insufferably smug! It's not the approaches. I fully subscribe to attachment theory, don't call myself AP necessarily, love the principles of playful parenting and positive discipline but have tried CC one desperate night.