The conflict between Blixes and Unicorns is mentioned in the books, both by Bracken and Vanessa.
We learned the basics of Blixes in books 2 and 4, with there being three types.
Lectoblixes: Drain their victims youth in order to make themselves younger.
Narcoblixes: control their victims in their sleepcan control victims in their sleep
Viviblixes: can control certain undead
Of these Lectoblixes seem almost like parasites for humans, definitely big threats to them. Canonically we know they have also hunted unicorns in the past, though they aren’t able to do much harm to unicorns due to how “pure” unicorns are.
It may have reached a point that they tried to kill unicorns to get at their youth or attempted other methods to lessen the intensity so that they could successfully drain the unicorns youth.
We know that Unicorns have been hunted by Blixes, though if this meant all Blixes (when only Lectoblixes seem to crave the Unicorns youth) or that it was just Lectoblixes but as they were the ones the Unicorns interacted with they shaped the Unicorns views of all Blixes, we don’t know.
Either way we do know that at least one group of Blixes have hunted Unicorns, and in turn the Unicorns hunted Blixes likely as a “preventative” method to handle the Blixes. They may have also been hunting them (especially Lectoblixes) because they attack and drain humans of their youth and likely kill many of them.
It seems their hatred is a mutual cycle of hunting, and without knowing more of their history we cannot say how much the Unicorns targeted the non-Lecto-blixes, and nor can we say whether it was justified.
In the end though, it seems to be a mutual hunting and the Unicorns reaction overall not unreasonable. They were protecting both themselves and humans from Blix attacks. Whether the non-Lecto-Blixes earned the hunting or were even primary targets, we don’t know and thus can’t judge.
