Balmoral does fully blame Foirtchern for Faolan's fate. Like yes, she did get thrown down there but he fully believes she could have changed things. She was, at least in his understanding of her, a Fateweaver. He does think that his existence narrowed and eventually closed that path and of course, he blames his 'father' for even proposing it in the first place.
Especially because he is so sure in his head that Foirtchern did not give a shit of her chances. Odds are together, they could have escaped. But he doubted that Foirtchern wanted to remain any longer than he had to. If he had to screw over some fae to do so, so be it. And even more...it's actually interesting because Bal has his own idea of what Foirtchern is like and he's never met his Abyssborn parent until his appearance recently. But it so happens, he's a lot of what Bal did imagine.
Which probably contributes to his disdain of his parent. Like being cause for Faolan's suffering alone was already terrible terms with Bal. Side note that yes, Faolan was just as terrible of a parent as Foirtchern to Bal. However a combination of an innate loyalty as a Harbinger to her and sort of seeing an 'idealized' version of her in his memory, Bal doesn't view her anywhere as terribly as Foirtchern.
The other part of dislike, I am finding, is because Balmoral can see himself within Foirtchern. And he hates it. He hates it so much. Because he's seeing it as 'this is probably how all of them (his enemies, those he's tricked, etc) view me' and honestly? He can't blame them for not liking him if that's the case. He would want to be rid of himself too.