Garen’s sword only has one edge that he can effectively deal damage or hit somebody, Jax’s lamp is a blunt staff that can parry and attack at the same time. With a staff like jax’s both sides usually have the same shape, so it doesn’t matter what side you use, you can easily block a swing from a sword (or AA in game) while simultaneously being able to attack somebody with the other end of the staff.
With garen’s sword you can’t do the same thing, if you try spinning around yourself while holding a sword you will find it very hard to block attacks. that is because you are already moving you will have to either stop moving and move your sword to the correct place to parry, or move your sword while spinning to block the attack. The problem with both options is that you will be using the only way that you can attack or deal damage (the sword) to block something.
So making Garen able to AA with his sword while he is spinning (which he uses his sword for) is super unrealistic and impractical and just doesn’t make sense at all, both in-game and in real life. Now if RIOT changed some of garen’s visuals to make him split his sword into two smaller ones while spinning, like in the god king skin, then this idea of Garen being able to AA while spinning might make sense.
If my realist viewpoint doesn’t help then here is another and probably more simple explanation. Jax’s e dodges during a channel then deals damage and stuns people in a radius at the end of the “channel”, so he isn’t dealing any damage with just the e channel. Jax can AA during the e channel to let him still deal some damage.
Meanwhile garen’s e deals continuous damage around him and he can’t block damage while spinning. So Garen can deal continuous damage with the trade off being that you can’t AA and that there is no dodge mechanic.
If you take the part out where you can AA during jax’s E then you get a pretty bland and uninteresting ability. And you take away what I think is a very big part of his late game damage. But honestly jax being able to AA during e is not that big a deal, usually a jungle jax will be using it to sustain better in the jungle, he usually will charge e while running towards an enemy so he can jump onto the target or near it to it and immediately stun them to CC them in a gank.
