Problem: I recently taught my wind serpent "dive" but it did not appear on the pets skill bar. I checked my train pet skill, and sure enough "Dive (rank 1) 15 TP" was in the box, and I was down 15 training points...so for others who have a similar issue, here's why it happened and how to fix it:
Why it happened: I believe the cause of this bug to be when you have a skill that is not on auto-cast as the last skill on your bar, and you train a new one, your pet will not automatically place this ability on his tab. My wind serpent had growl and bite on auto, but LB on manual cast so I could get my one LB in per fight during PvE (it uses up all my focus on this rotation as it is). So when I tried to teach it dive, it didn't put it on after the manual LB.
How to fix: To fix this, simply go to your pet skills tab (hit 'P' to open your skill tabs, at the bottom it should say 'spellbook' and 'pet', click on 'pet'), and drag down the skill that did not get put on your pets skill bar.