Because the child probably looks promising to their mothers, who project what they wanted for themselves, steering their girl through a life that maximizes what they think is something they missed out on, and then wanting to vicariously live through that. The child is the extension of the mother, fashioning her ideal sense of her unmet self in the child.
The mother truly believes she is doing the child the biggest favor. To her, it elicits the momentum for the path to success in the aspects of looks. It's basically that woman's best idea of love, by giving her daughter what she wanted and believes is a worthwhile life. It's not limited to a child beauty pageant but a whole life path, starting from that.
