“Real” Father

My friend who re-married after her first disastrous marriage recently had a showdown with her only child, her son from her first marriage. The son, now a young teen on a visit to his grandparent’s village just found out while being teased by kids of his own age that his father wasn’t his “real” father. Who is a “real” father? Is he the one who left/donated his “sperm” or the one who gives his name and raises the child? How would those other kids have known about this fact as my friend had re-married when her son was just a baby which means that the other kids too would have been babies too or yet to be born? This leaves us with the fact that the elders / parents are the ones still talking about my friend’s second marriage and that too in the presence of their kids. Why is it a stigma to marry a second time especially for a woman in most of our cultures?