To be unreasonable means acting in an irrational way. Your expectation that your favorite team will win the Super Bowl every year is unreasonable.
When someone's unreasonable, they're not using reason, or common sense, to make decisions or demands. Add the prefix un- to reasonable, "having sound judgment," and you get an adjective that's perfect for describing illogical behavior. It's often used for a certain kind of demanding stubbornness too: "It's completely unreasonable to make your server take your soup back five times to warm it up a little more."