How do these things seem to get turned around?

They speak to a deeper truth than the originals. People regularly fixate on their parents as idols and seek out peers/romantic partners that share these traits. Besides, the original allegory of Oedipus implies a man who is actively fighting is destiny - fleeing his found family, precisely because he wishes to avoid prophecy - but stumbling into it because "destiny" compelled his actions. The idea that you cannot escape this destiny is in line with the Freudian instinctual response.

Past that, a lot of the modern turns of phrase are clarifying. Jack of all trade*, master of none* reminds the listener that one's time and talent are are finite resource. "I also hear it said that kin-blood is not spoiled by (baptismal) water" reminds the listener that one's old family roots can have a firmer hold than a newly discovered religiosity or traveled distance (which may alternately assure or question one's loyalty to a tribe based on their family origin).

"Curiosity killed the cat" probably got the turn of phrase just because worry killed the cat is less in line with a modern cat's understood character.