No the men cant hold the babies - only the Birth Mother can hold babies
If the bar is the "Breed" Skill level bar...
well CARING for a baby does NOT increase the "SKILL" of the "PARENT", Skill is determined by the initiation and successful completion of the "act"... If BOB "kisses" SUE, and Sue accepts his advances .... Bob gains Breeding Skill, Sue doesnt... even if a child is produced...
So Villagers who "play the field" and initiate a lot of embraces... will be the ones to become MASTER PARENTS... We know, it makes no sense... but this is how the game is programmed... maybe in the future it will be changed?? No one knows...