Are we likely to side with the party of the president that we came of age with?

I came of age (16-24) with President Bush in office. I considered myself very liberal then but by the end of Bush's presidency, I realized I was actually very conservative.

I've noticed that my dad around the same age as that when President Johnson was in office and he's very liberal. My mom was that age when Carter was in office and she's a Democrat - although not as liberal as my dad.

I've noticed this same trend with various other family and friends of mine. Is this a thing or is this just a coincidence?