Why do fighters have better shields than supports?

Yasuo and shen don't even carry shields wtf u talking about? They have SWORDS

Ba Dum Ts

Because riot wants only bruisers/flashy champs to be playable.

Shen has three, and one of them is global, and teleports him across the map. He is excused.

There's actually been debates about Wind Wall vs Unbreakable and I believe the consensus is Unbreakable is WAY more valuable when you factor that the shield can be repositioned. Big deal especially the higher up you go. It was a debate but in my mind, Yasuo is excused for being fundamentally different enough.

As for Panth, he is a squishy melee champion without it. Pantheon also lacks the mobility and flexibility of, let's say, Zed. This is where the cohesiveness of Pantheon's kit is a huge element in this discussion and comparison. One thing that really damns it however is that it does not destroy Skillshots, putting it as an entirely selfish shield. Even if you can argue it's a "better" shield in terms of protecting Panth than Braum, this generally follows the logic of their classes since Panth is definitely worse at defending teammates.

Why does support have better AA modifier than a fighter? Renekton vs Shen?

Since when Shen is a support by design? You can play Teemo support~ does not make him 'a' support.