The aesthetics of having your character become twice as big when tanking or switching stances aside, I just can't see cavalry being more defense-oriented than infantry.

Cavalry are closer to DPS in terms of the role they play in armies. They attack front the flank or back. Attacking from the front is a great way to lose your horse or get impaled by a spear (assuming you're fighting against an equal). The horse is really vulnerable and there's no way you can carry a shield to protect them all the time (imagine trying to lift a shield large enough to block arrows like in 300 or forming a tortoise shell formation of shields like in Gladiator while mounted). Instead, cavalry outruns any enemies that chases them and then runs back in to attack from the flank or rear.

If anything, the chocobo should be out for DPS and gone for tanking. it is a personal preference though.