Arbiter's shadows can't overpower normals, or is this for everyone?

I’ve been recently playing the hell out of Arbiter and it seems that whenever I use any of his shadow attacks, they can be stopped by normal attacks like for instance a MP from Rash or a simple smack in the face by Aganos (I do know that Aganos can do that to every character, I’m just trying to state my problem). But aren’t shadow attacks meant to overpower normals? Because I’ve been playing Ranked Leagues recently (still haven’t got to Killer because -->) and there’s a lot of trolls, people spam attacks, corner you and don’t let you free out of that corner, taunt and teabag etc. And I try to ignore that when playing Arbiter of pretty much every character. Sabrewulf’s Leap can stop Arbiter’s shadow attacks.
If this is meant to happen, then I’m sorry, I didn’t know.

There are different priorities for different moves based on their properties and what they could possibly chain into. Shadows will not always be the best version of a move.

No they arent, they have different properties:
Shadow thruth seeker its projectile invulnerable, use it to punish them
Shadow mercy demise its good during lockouts for damage, but has no invulnerability
Shadow prophet bane its vulnerable in its first frames, but once invisible, tracks and its fully invulnerable
Shadow energy shield works as a reversal, knocks on hit, and deals 0 damage. Your best “get off” shadow move

Other characters have different special properties in their shadow specials, depends on each move


It’s true that, technically, shadow moves > normal attacks in the input priority system. However, that is only for when the moves trade (ie, strike on the same frame).

Both shadow truth seeker and shadow mercy’s demise are fairly slow on startup (Arbiter rushes close to his opponent first), so a normal attack will interrupt the shadow move before it comes out. As Dayv0 said, these attacks don’t have hit invincibility so they won’t go through attacks normally.