Recall that at the placenta, the mother's blood comes incredibly close to touching that of her baby - but never does. It passes so near, however, that for the purposes of this thought experiment, we can think of it all as one large pool of blood.
The mother's haemoglobin must obviously start out with the oxygen - only she is in a position to pluck it out the air via her lungs (the baby's lungs are filled with fluid!). Now how is this oxygen to get to the baby? If the baby's fetal haemoglobin had a lesser affinity for it than the mother's adult haemoglobin did, then not much oxygen would get across the placenta, would it?
No, fetal haemoglobin must bind oxygen more avidly than adult haemoglobin, so that it can strip oxygen off the mother's red blood cells, and carry it to the baby's own greedy body.
(Mothers take note: once again your cute little baby is sucking the life from your body. Parasite.)