Oh, it doesn't bother Loki in the slightest. He's heard worse, and from people whose opinions he respects much more than he does Skaði's--not that he listens to those opinions either, but her words mean nothing to him at all. She's a child lashing out, and nothing more.

Pyrrha, on the other hand...

This is for all the times he couldn't protect her, everything she's had to go through because he was unwilling or unable to take a more direct approach with her. She doesn't deserve this, and Skaði is going to pay for hurting her.

"Shut up shut up SHUT UP!" she shouts, and with a burst of anger Pyrrha didn't even know she had, Skaði is briefly engulfed in flames.

It doesn't last long, and it doesn't leave any marks, but for a few moments it is excruciating.

And that's what happens when Pyrrha snaps.