Why do we say "She pointed "to" herself" and "She pointed "at" me"?

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You could also say "she pointed to me" and that would also be okay.

Both "point at" and "point to" generally mean the same thing. "To" is a little more specific than "at". They are pretty much interchangeable.

For example, if you "throw to" someone, you are throwing it specifically to their hands so they can catch it. If you "throw at" someone, you can be throwing to anywhere on their body - much less specific.

When it comes to pointing, "at" is more accusatory than "to".

Example:
"Which one of you broke the glass?"
"We pointed at each other"

"To" is for much softer situations. Example:

"I asked her which flower she wanted and she pointed to the red ones".