A. because Congress made it that way. The credit offsets some of the cost so that both spouses can work, since there are so many two-earner families. A stay at home parent doesn't have costs to offset.
B. because there is never a tax break from income you never got and tax you don't pay. You don't get anything for the value of your own labor unless someone pays you for it and then you pay tax on that income. If you work for free (for anyone, not just your own family) there aren't any tax benefits for that.
