Just a few more things to add to what NintenNerd already wrote:
If one is a senior (Otokitchi or Ojitchi) then s/he will mate only with another senior of the opposite gender.
Even if the characters are suitable for mating, it could be that they don't love each other. Just keep connecting them. Within about 20 connections, their relationship level should reach high enough that they'll fall in love and mate.