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Where does the 3 times cursed part come from. I can only think of two:
1. Betraying the Emperor.
2. Turning their backs on Abbbadon

Maybe I'm way off on this but it's something that caught my interest. I wonder is the third is failing Horus?

Gonna need some context here...

You're talking about the Black Legion right?

How about betraying their brothers instead of Abaddon?

And the Imperium, and the Emperor?

I think "thrice cursed" is just a general term for really bad people.

This seems to be a chaos used insult directed at either the loyalist or the alpha legion.

Alpha:

Betraying the Emperor for aliens, betraying humanity for aliens, the forces of chaos for aliens.

Loyalist: betraying the crusade, betraying their fellow legionaries by not joining horus, being blind in ignorance and betraying truth itself. I'm guessing that's what marduk meant when he used it against the alphas and ultras.

I'd say the first statement it pretty true, the alphas are the true traitors of 40k, everyone else just takes what side that happen to fall under, as far as the loyalist they fought for what they thought would be best for the imperium, same as horus, same as the emperor.

Mankind? Emperor? and Chapter?

Perhaps it's allying with forces of "Daemons, Heretics and Xenos"

I think you'll need to post the fluff for us to have a better idea of what it is though.

The 'Thrice Cursed Traitors' are those members of the Sons of Horus that did not agree with Abbadon and did not join the Black Legion, instead remaining true to the memory of Horus and forming the True Sons, Wolves of Horus and Sons of the Eye.

No, just term for bad people. ie: THOU THRICE-CURSED DAEMON SCUM!!!!