Question: Potential energy can be thought as the amount of work that the force can potentially do on the point because of its position. $$W=-\Delta U=U\_{initial}-U\_{final}$$

A positive work done by a force translates into a negative variation of potential energy. That sounds ok, given the interpretation of $U$ stated above. If a force does some work, then the "potentiality" of doing more must decrease.

But the equation says also that any time the force does a negative work, the potential energy increases. Why does this happen, in the light of such interpretation of $U$?

Answer: 
If a force does **negative work**, it is in fact trying to work against another force, doing **positive work**.

When you lift up a book from the floor, gravity does *negative work* on the book, while you do *positive work*. And the books rises higher up, so $U$ increases.

* Negative work just means "**receiving**" instead of "**giving**" away energy. Which basicly is the same as saying that *something **else** is doing work on it*.

There is not more to it than that.
It is just a convention. If we would use the opposite convention, we would get for conservative forces 
$$\vec F=+\vec\nabla U.$$
You can easily see (think in the one dimensional case) that the particle would move to points of maximal potential energy. This only sounds strange because we are used to the opposite.
The mechanical energy principle would retain its form, 
$$\Delta E=W\_{nonc},$$
as long as we redefine
$$E=K-U.$$