Absolutely Agent and mathanxiety
Shit, I'm not saying that there aren't shit men out there that compete with their children for attention. I'm just saying that there are women who become completely obsessed with their own children and completely ignore their husbands.
Whether a man is being a childish asshole, or a nice bloke who is now being treated as surplus to requirements, depends on everything else that is going on in that home.
Of course it's valid (and interesting) to talk about the ways we love our children, and how that compares to and differs from how we love our partners.
I do think the standard MN "you come second in the pecking order" is very reductive and simplistic. A good father's interests are almost never in competition with his own child's interests. If an otherwise good man and devoted father feels pushed out of his own family, the first thing to consider is whether he has good reason for those feelings.
Making a Dad feel included isn't putting him ahead of the children. In fact both interests are equally served by making that effort, because children love their Dads. In a good relationship the mother is also best served by this course of action, because she wants what is best for everyone in the family.
But where the woman is the self (and baby) obsessed narcissist, she will prefer that her children love her the best, and get off on her supposed martyrdom to her kids. Women can be assholes too.
I think a family pecking order of importance is as good as useless in a happy family. Family life is about balance, not hierarchy.
To go back to the fire scenario (that annoys me so much) - you help children first because they are vulnerable, and your job as a parent is to look after them. That isn't the same as more love. The way I feel about my children is a deeper love than I had ever experienced before, but their arrival changed my love for my husband too. They are the physical embodiment of our love for each other. He is central to this family. I feel no need to relegate him.