Seeing a problem from the other person's perspective has been widely studied and shown to be related to prosocial behavior (i.e., being nice to other people).

I think you stepped on a landmine by thinking that the half full/half empty thing proves that contradictions can be true. "half full" and "half empty" are two different ways to say the same thing: it is filled to 50% capacity.

One of the basic principles of logic is that contradictory things can not both be true. The most frequent problem that I have seen with new philosophers is related to making references to the real world with an inadequate operational definition. (note that logic deals with abstract things that are not in the real world and science deals with things in the real world).

The classic (false) example from new philosophers is similar to your example: "The shirt is blue" and "The shirt is not blue" are both true when you have a blue and white striped shirt. The problem is that the person did not have an operational definition of "blue shirt." If the definition is not clear, your scientific study loses validity.

If you have access to a university library, and you have lots of time on your hands, you could read about some challenges with construct validity (in psychology) and the challenge of creating an operational definition. This article is a historically important step in developing those ideas: article reference