Indeed. I find it useful to remember that points are fictional things except perhaps at the end of a sword.
I’d often hear someone say to me, “You’re missing the point” if I’m not agreeing with them.
In my mind I think two things right there:
a) Spacetime points are useful yet also constructed fictions.
b) Points in a conversation are also useful but constructed fictions.
c) A point at the end of a sword pierces skin.
d) i don’t want to get the point. of either the a, b, or c type.
All that being said, there’s a social thing that isn’t unimportant: friendship. A constructed point of mine? Yes. But just as mathematicians believe in points-as-real, I believe in friendships as an important point to consider.