If I'm at dinner with a casual friend or workplace peer, my family and even critical professional activities are more important than them to me. That doesn't make me more important than them, though, which is what enrages so many people, sure that they need to put people in their place.
No matter what subtleties you wrap the difference in, relative importance is what you're communicating to everyone else at the table whether you intend to or not. If that's your priority then so be it, but don't be surprised if people who prioritized being present at dinner aren't fond of your choice.
I'm not trying to change you though. Like I said before, I just wouldn't want to eat dinner with you if you couldn't leave the phone alone.
I think it is a confusion of expectations that creates the conflict. You expect it to be understood that this is how you prioritize. Others may not have expected the same priorities.
I love putting my phone away at meals, it's a good time to be social and set aside the demands of professional life.