My season allergies started when I was about 30 and didn't start gettng really bad until age 35, so from my limited experience, it's possible for allergies to develop seemingly out of nowhere and/or to worsen over time. My allergy symtoms also change from year to year. Some years, I have itchy, watery eyes. Some years I have a lot of sneezing. This year, I had a mean case of post nasal drip to the point that I had trouble swallowing. Some symptoms are easier to tolerate than others. Some years my drugs work better than others, too. It's a moving target.
It's one thing to blame allergies when that's really not the reason a person is getting rid of a pet. I think we both have a problem with that. But your original post seemed to suggest, at least to me, that people with pet allergies should just take a drug and deal with it. I'm sure some do and feel like it's an acceptable solution. Allergy meds do work for many. For others, however, rehoming might either be the necessary or preferred way to deal with the problem.