I used to have that problem a LONG time ago. Aaron and KojiroTakenashi are correct about it being the Chocobo's behaviour.
The solution, is too feed the chocobo in question. A LOT.
Probably after giving it like 5-10 grains (I forget which type in particular, but it might be Mimmet [or however its spelled], unless that turns out to be one of the super-duper-rare greens.....yes, I haven't played the Chocobo area in a long time...
Either way, its stemming from the fact that because you caught it, and it used to be wild, it doesn't want to obey your commands. The one you raced with the first time around was an already-human-trained one, hence its obedience.