Fair or not, on a flight the crew is in charge. I can't tell if this was a request of the "would you be willing to" variety or if they were basically telling him to move. If it's the later, your only recourse is to leave, or comply with their request and try to get compensation later. If it's the first, you can stay in your seat, but there was usually a good reason they were asking you to move and you're likely to be stuck with a solo child next to your or some other negative. In fairness, I would have no problem rejecting a request to switch to a middle seat these days since it seems less safe.
But flying is stressful under the best of times and these are not the best of times. It's worse if you're also worrying about something else like your animals . I don't know the story of the tiger guy, but generally, in a fight with flight crew, you're going to lose.