I came across the word "budge" in a dictionary, and it said about this word: "Usually used in negative". Why does this specific word always come in negative form?
Generally, you're trying to move something. If something just "budges" that means it moved so slightly as to be an insignificant change in its position. When trying to move something, it is often useful to indicate that it didn't budge and thus one did not even get close to the desired movement. But it is rarely useful to indicate that something budged because merely budging is so insignificant.
It's perhaps much the same reason we more often point out that we don't have even a drop of water than that we do. A drop is so close to none that having it is not worth pointing out.