Women have the fit inherited trait of being neurotic so that they are more aware when tending children, and get very worked up over their babies.
Men, not so much. Men look after the woman to look after his kids. Always has been that way. Societal norms evolved from biological norms, not the "patriarchy"
Jordan Peterson often references evolutionary psychology and Big Five personality traits, pointing out that, on average, women score higher in neuroticism (which includes anxiety and emotional sensitivity), while men score higher in assertiveness and risk-taking. He argues that these biological differences influenced the traditional social division of labor and parental roles.
In his book, 12 Rules for Life: An Antidote to Chaos, Peterson explains much better than I can how evolutionary pressures shape human behavior and social structures. Jordan often discusses the biological basis of gender differences in his debates and lectures, often referencing scientific studies on personality, evolutionary psychology, and child-rearing behaviors. If you’re looking for a specific source, you can google many of his YouTube lectures and podcast interviews that touch on this topic in depth. You can also look at some of his conversations with Joe Rogan and his debates with figures like Sam Harris where he also dives into these ideas with more detail.