As a healer who switched to tanking for Stormblood, I've seen both sides of this, but I'll comment from a healer's perspective.

I can't speak as to your being kicked. You may have felt the healer could handle it, but maybe the healer felt differently?

Yes, you're a tank, you can take more and bigger hits. But that doesn't mean you HAVE to. Many cases, you can move out, and back in when it's safe and the boss won't move. But if you have to move, so be it. Like others said, the DPS should know how to adjust. Yes, there are some things you can't avoid, or times when you have to take a hit. That's okay, that's what cooldowns are for.

In short, throw your healers a bone and dodge when you can. It helps us to help you.