Visualize the jet from top down, then visualize the crosswind from the right.
Now think which part of the aircraft offers the greatest amount of resistance to that wind. Correct, it's the bloody great big tail sticking up at the back end of the jet. The wind always tries to blow it around so that the tail is at the back and the nose is pointing into the wind. That's called "weathercocking".
With a right crosswind, that means the nose of the aircraft is trying to pull to the right on takeoff. Hence, you have to use left rudder to counteract it.
