There exist an infinite number of planes through any ony point.
There exist an infinite number of points through any two points. (Rotating around the line through the two points)
There exist exactly one plane through any given three points. (Take those planes rotating around line through the two points and rotate until it touches that third point.)
As Plato pointed out, your question is baffling.
Let's look at a simpler problem.
They say: there is exactly one line passing through two distinct points.
Does that mean each distinct point has a line?
We are given two distinct points.
Code:P * Q *
There is exactly one line through the two points.
Code:/ / P * / / / / / Q * / /
You ask: Does each point have a line?
Answer: Um . . . yeah . . . I guess.
Code:/ / P * / / / / Q * / /
What's your point?