For light armor characters, you'd THINK the left path would be a better choice... but actually the right-side path is still better.
If you go up the left, you'll gimp yourself on damage because the highest tier weapons are only on the right (daedric + ebony). You will not be able to upgrade daedric or ebony weapons through smithing very effectively due to lacking the respective perks (in fact, if you go left, the best weapons you'll have after using the grindstone are going to be glass weapons).
On the other hand, if you go up the right, you'll be able to have the best light armor in the game (you can make dragon armor with just 1 extra perk), AS WELL as being able to make and improve twice as much the best weapons in the game.
Would have made much more sense if you could go to daedric from dragon armor (going from the left) but you can't.
TL;DR: right-hand smithing path is better than left-hand path for everything even for light armor players.