What is someone who for non-malicious reasons always interprets words in the least generous way?

Cynicism: Assumption of the worst about people or the outcome of events.

There is a small difference between cynicism and pessimism. A cynic assumes the worst, but analyses to find if the worst is true. A pessimist, on the other hand, is negative right from the start to the finish, and may not necessarily delve to find if his assumption is true.

Cynicism = skeptical objectivity - Trust but verify. Pessimism = negative subjectivity - It may not be so.

I'd call that pessimism.

an inclination to emphasize adverse aspects, conditions, and possibilities or to expect the worst possible outcome

According to wiktionary, a cynic is a person "who believes that all people are motivated by selfishness" or "whose outlook is scornfully negative." This is a bit different than what you asked about, even though the previously-suggested word cynicism is right on-target because it includes among its several senses "an emotion of jaded negativity, or a general distrust of the integrity or professed motives of other people".

Also consider bloody-minded, "behaving in a way that makes things difficult for other people; refusing to be helpful" and paranoid, "exhibiting extreme and irrational fear or distrust of others".

I would say "negatively biased". Biased means that everything else being equal, the alternative(s) towards which you are biased get higher chance of being selected. As for example, whenever there are two equally likely interpretations of your friends behavior, you tend to pick the one that's more negative.