The security of an infant's attachment to mother and the sensitivity of her care go together. Stress, including stresses that lead to insecure attachment, damages an infant's capacity to learn.
That is to say, if a baby lacks a sensitive response from Mum it becomes stressed and it's mental development is slower. The baby, in this view, needs to feel securely attached to its mother.
I've highlighted this quote because it is so out of step with modern day liberalism. Liberals like the idea that gender is something to be overcome, and so they tend to see men and women as being interchangeable within the family.
But in Penelope Leach's view, babies have a particular need for their mothers. It is a secure attachment between mother and child which is important. Mothers, therefore, can't easily be displaced by either fathers or professional child care workers in the lives of their infant children.