Why does my manual transmission have trouble shifting from 2nd to 3rd gear in a 2001 Ford pickup truck?

Why does my manual transmission have trouble shifting from 2nd to 3rd gear in a 2001 Ford pickup truck? - 1

Most likely cause is a bad synchronizer in the transmission. Prior to the invention of synchronizers shifting was a process of shifting to neutral, releasing the clutch, revving the engine to get the input and output at the same speed, depressing the clutch and shifting to the next gear. The process was called "double clutching" and required a bit of experience to accomplish without gear clash.

Either air in the hydraulic clutch. Broken release bearing fork, warped pressure plate or you already wore out the sycronizers.

Probably have a bent shifting fork, a bad clutch, or really worn out gears.

You can get around it by depressing the clutch, go from second the neutral, let the clutch out, put the clutch in, and shift to 3rd. That can exited the life of the clutch a few thousand miles.