User blog comment:IamJakuhoRaikoben/Chapter 411: Quid Pro Quo, Review./@comment-4449950-20141201232911/@comment-7418318-20141202233205

But isn't their Curse the most defining thing about a Demon? Thus if you want to be able to defeat them, you need some kind of defense against their curses.

A Fire Dragon Slayer is able to eat Dragon Fire, the Flame God Slayer said he was able to eat (and produce) God Flames, so if the other Slayers can eat what the being they were created to destroy uses, the logical conclusion would be that Devil Slayers are able to eat Curses, since that's the main attack method of the Devils.

And with Natsu being able to eat Lightning and Gajeel Shadow, despite those not being their own element, I don't see why an Ice Devil Slayer shouldn't be able to eat a Thorn Curse. Of course both Gajeel and Natsu needed a lot of experience and growth before they could do that, but I think this instant mastery has been discussed enough already.