It

This is what I would say:

I know you want to see it. I'm not going to show it to you, though.

Are these all acceptable and can be used interchangeably?

I'm not going to show it to you, though.
I won't show it to you, though.
I'm not showing it to you, though.

Why do native speakers use verb+ing a lot in cases like this one? Thanks.

All are acceptable. They have different nuanced meanings, so they are not strictly interchangeable.
Another option: I will not show it to you, though.

whatchadoinWhy do native speakers use verb+ing a lot in cases like this one? Thanks.

Probably because the progressive refers to a longer time period than the simple past, present, or future.

I don't think I understand these so I'll try to "analyze" them.

I'm not going to show it to you, though. - How about this one?
I won't show it to you, though. - This one sounds like a refusal to me.
I'm not showing it to you, though. - This one just tells me that I don't intend to show it to you.

________

School starts tomorrow.
School is going to star

If I were going to put these in a book...

I'm not going to show it to you, though. - How about this one? Teasing, tantalizing. Inviting the other person to be more curious.
I won't show it to you, though. - This one sounds like a refusal to me. Yes, secretive, defensive.
I'm not showing it to you, though. - This one just tells me that I don't intend to show it to you.