I like animals a lot, but a LOT of people have allergies, and it's just plain obnoxious (at best -- medically dangerous at worst) to have animals in the cabin. The air in a plane ALL mixes. You can't just say, "Ask to be reseated further from the animal," depending on level of allergy.
I don't know how it came about that people were allowed to bring their cats and dogs in the cabin. Perhaps it's always been allowed in the US. In Ireland (I think in Europe in general, or maybe even more globally), if you wanted to bring a cat or dog with you, you put it in a really sturdy travel carrier that was designed to be put in the luggage compartment (I believe there is [was? if so, airlines need to put it back in!] a heated portion of the luggage compartment for precisely this reason), and ... that was it. I know people are very attached to their animals (I would rather have my cat with me if I were travelling by plane), but, well, tough. It's not fair to other passengers.
I have had occasion to be travelling with someone allergic to cats/dogs and have somebody bring an animal on the plane, and it is not a good thing. I was reminded of this when, a few minutes ago, an old woman was wheeled up in a wheelchair and seated a her bag put up on a chair beside a girl who was a couple of seats from me. The girl quickly realised something was wrong, and asked, "Is that a cat...? I'm deathly allergic!", and had to leave immediately for another part of the gate area (or further; didn't see where she went). "Deathly," was probably an exaggeration, but ... this really still shouldn't have to happen.