Can't learn the riding skill

I have reached level 20 as a blood elf mage, but when I go and try to learn the riding skill to be able to mount, the skill insn't available for me. I have never seen this happen before, is this a bug or is there any other way to learn the skill?

image of the mage trainer:
https://imgur.com/a/XBfu0FD

You don't learn riding at your class trainer. You learn it at the riding trainer. For belf that trainer should be right outside the city - exit the city gate and go left.