Celebrating a Mother's Day really makes little sense, because the mother-child bond needs no social support. It represents instinct, the work of hormones and hard-wiring in the brain.
What is needed -- desperately -- is social support for fatherhood. Fatherhood is a social institution, fashioned together by innumerable laws and customs.
Why would a man, following his biological programming, bother with fatherhood? Why would he stick with one woman to help her raise his child? Why would he allow his disposable income to be split in half or less? Why would he give up chasing other, more attractive women? Why would he risk financial and emotional ruin in case of a divorce?
The answer is because he grew up in a culture that gave special meaning and reverence to men -- fatherhood.