Why "reduce to", not the other way around?
There are several different types of reduction, but generally, if we say we reduce problem A to problem B, it means something like:  if we had a way to solve B, we could use that to solve A.  Some reductions may allow to use B as a black box.  Others might require that "yes" instances of A map to "yes" instances of B, and that "no" instances map as well.  Or, it may be something simpler, like "hey, I already have a great solution to problem B, and now with just a simple transform, I can use it to solve problem A."
In all forms, it implies something related to "we could solve A if we had solutions to B".

What that means has something to do with what is known.  If B is an easy problem to solve, then A reducing to B tells us that solving A is no harder than solving B, plus doing the reduction from A to B.  In that case, an easy reduction, to an easy problem, proves that A is easy.

On the other hand, especially in the context of hardness results, we would usually reduce a known difficult problem (A here) to B, and that would show that, because A is hard, but transforming an instance of A into B is easy, B must also be hard, because if B were easy, it would give a solution to the known A problem.

So basically, for an easy reduction from A to B, it proves 2 things:  A is not harder than B, and B is not easier than A.  Yes, those are the same thing, but usually, you only care about one of them, depending on whether you know A to be difficult, or B to be easy.