No, that's not at all what I'm saying. I'm saying that if someone seated next to me is allergic to my pet (or for whatever reason doesn't want to sit next to it

No, that's not at all what I'm saying. I'm saying that if someone seated next to me is allergic to my pet (or for whatever reason doesn't want to sit next to it), then they could relocate either me or that person so that we're sufficiently far apart not to cause any issues. The argument presented to me in the past (and also the argument in comment I was replying to) is that since some people are allergic to pets or otherwise dislike them, we should completely disallow traveling with pets in a blanket fashion. I'm simply saying that I think that's too extreme and that a middle ground can be found. If we're going to completely ban pets on airplanes, then we should consider also banning flying with a cold because of immunocompromised people (in fact this is perhaps more warranted given the severity of the situation).