"Maybe that mantra has something in it you should try to understand? What you think Christmas is about isn't necessarily what everyone else thinks Christmas is about.
If I walked through a church you wouldn't presume I was a Christian, why does the fact that I live through Christmas make you presume that I think I am?"
I think Christmas is about the celebration of Jesus' birth. Full-stop. There is no other Christian way of seeing it'
That's fine, that's your Christmas, that's what you do with it. That's not my Christmas, at least in part because I'm not a Christian.
Your second point is unclear.
Christianity, as I understand it, isn't in the actions. I'm not a Christian because I kneel in church, I'm a Christian if I accept the idea that Jesus is real. I'm not a Christian if I try to be a good person, I'm a Christian if I try to be a good person as Jesus instructed.
The reasons you do things are what makes you a Christian, not the things that you do. I partake in Christmas celebrations for many reasons, but none of them are because I think Jesus was born then, or indeed because I think Jesus was born at all, or because I think of Jesus at all. I didn't choose to call it Christmas, just like I didn't choose to name days after Thor and Odin - I've inherited those cultural tropes, and I accept that are part of my history.
Christians never owned midwinter, never owned the concept of giving gifts, never owned the idea of celebrating with family and friends. That we call one particular time-based instance of that 'Christmas' because Christians long ago wanted to co-opt pagan midwinter festivals doesn't mean only Christians can do anything at the end of the year.
O.