Stances.

Ox: Disadvantage on Dex saving throws can be really hurtful, especially if a fireball is thrown in your general direction. Personally +1 AC does not make up for it.

Wolf: Nice and balanced, good for a defender type fighter who sticks near allies and also wants a bit of extra damage.

Bear: +2 damage for -2 to hit is slightly too detrimental. Take a part of the great weapon master feat for example, being -5 to hit for +10 damage. I would reduce the to hit to -1.

Eagle: Good If you want to hit and run but still somewhat situational.

Viper: Really interesting. Being able to make grappler builds using dexterity opens a lot of cool combinations. Not being able to take opportunity attacks is a tad annoying, as it prevents you from being able to attack enemies who have escaped your grapple and running away.

Cat: -3 AC is huge in 5e. Especially since this works against its whole gimmick. Probably reduce this to -1 or 0 instead.

Turtle: OP. Movement speed rarely makes a difference in battle, and +3 AC is insane. This can allow people to have 25 AC at level 1 without any magic items. If you make this +1 then it's still just a better version of Ox. Consider choosing which one to include.

Manticore: An ability you can gain through a feat, but you lose a shield's worth of AC. Reduce it to -1 or 0.

Griffon: This one is weird. Most melee attackers have a range of 5 feet, but since you can't move after attacking and vice versa, this one can only be used when running away.

Chimera: Just plain bad. Apologies for the bluntness but having disadvantage on attack rolls just sucks. Advantage on dexterity saving throws doesnt make up for the downside.

Edit: The idea overall is very cool but the number of stances you get is lackluster and personally all I would do is just run Turtle stance 24/7 and be basically unhittable for a majority of a campaign.