I think you’re being overly picky and cherry-picking your argument here. I don’t know anyone who thinks that child rearing is not hard work, and all agree that it is valuable.

But in the context of this discussion, “productivity” is an economic term for the production of goods or services, and the generation of income for the workers. Child rearing does neither of those things directly, so as an economic activity, it doesn’t register and thus those parents are not part of the workforce. Again, that does not mean it is not a valuable thing to do for both the child and society, but it also does not directly add to GDP, generate income taxes, etc.