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It's not that black holes prefer a direction, it's just that they have a direction at all. It's one of the very few observable properties of a black hole.

If I'm following correctly, the "we're inside a black hole" idea is a major reach, connecting at least two unrelated concepts (black holes could contain baby universes; black holes have spin). But it's a really interesting idea and not obviously wrong.

Is inside the article:

"A preferred axis in our universe, inherited by the axis of rotation of its parent black hole, might have influenced the rotation dynamics of galaxies, creating the observed clockwise-counterclockwise asymmetry,” Nikodem Poplawski

I think it would be more that the entire universe is in a black hole spinning in a certain direction.

Exactly and anything new entering the spinning black hole is likely to inherit its spin.