I've never wondered why coming out (to me or others) was important to someone. Never. Of course it's important. It's a part of who you are. It's a part of your self-identity.

I mean, if someone genuinely feels it's not important, that's ok too, but I think feeling that it is important for the people in your life to know this about you, and for you to know that they accept you, is entirely normal and understandable.