Ah, Owain. He's special. With a capital L.
All of the children are tied to the same mother. So Lissa will always produce Owain, regardless of the father. The only exceptions are Robin and Chrom. This is because Chrom must always have Lucina as a child, Robin will always have Morgan as a child; therefore allowing only those two to produce siblings.
Chrom allows the Lord class to be handed down, which makes Cynthia(Sumia), Kjelle(Sully), Brady(Maribelle), Inigo(Olivia), or male Morgan(Robin) have awesomeness through Aether and Rightful King skills.
Robin passes down the ability for the sibling of male Morgan to wield any class. Having the ability to change a character to any class is awesome. The only times Morgan will start in the base class of tactician are either marrying Olivia, Lucina, or Chrom though. All other times, s/he will start as the opposite spouse's base class.
The only thing the father does for any other character is hand down the stats, which absolutely sucks and makes me upset considering Robin has a different set of quotes in the CBAs than Mark does. I began trying to figure out proper pairings because there is only one line and because I'm strangely obsessive with doing this with all my Fire Emblems. Stupid, I know. But I do it anyways.