Why is a crossbar in football/soccer called a crossbar?

Same reason as in rugby. It runs across between the two upright posts. And its a bar. The simplest form of goal is a couple of coats on the grass. To avoid the endless arguments about whether the ball went between the coats or over one of then, posts were used. At first, just withies - thin saplings. Even there, there is a problem. Did that very fast ball go inside or outside the post? So nets were introduced. If the ball is in the net, it must have gone between the posts. The crossbar helps to keep the uprights upright, and to support the net. It also keeps the ball to within reach of the keeper. Without it, the arguements and high kicked balls would be endless. https://en.wikipedia.org/wiki/Football_pitch#Goals etc

In American football, the crossbar not only connect the vertical goalposts, it also connects to the stanchion that supports the entire goal assembly (in goose-neck type assemblies, whether they be single-stanchion as in the NFL or double-stanchion, as at Doak Cambpell Stadium in Tallahassee). In double-stanchion assemblies, where the vertical supports are also the goalposts, the crossbar simply links the two supports.

As opposed to soccer, where the crossbar forms the upper part of the goal assembly, in American football the crossbar forms the lower part of the goal assembly. That is, a ball kicked UNDER the crossbar is considered no good. The reference link shows an American football goalpost assembly.

https://www.reference.com/sports-active-lifestyle/dimensions-nfl-goal-posts-36aaa8515764be7b#

I've often wondered if rugby and American Rules were created by people who couldn't keep the ball down......