Sorry, this sounds like the "tender years doctrine". I refuse to acknowledge that women are predisposed to taking care of children who are younger. Both men and women (as parents and teachers) have a role in the entirety of a child's life. This notion that men are unnecessary at certain stages of a child's life is harmful.

Men can cognitively recognize that young children need to be treated with more tenderness than older children.

I really, really, really dislike what you're implying. It puts too much burden on women, and it robs men of a critical part of being human. Men are capable of empathy, nurturing, teaching and being patient. Denying that is so dehumanizing.