Prior to vaccination, mothers were naturally immune to diseases and passed that immunity to their infants via placenta and breast milk. Vaccinated mothers may have vaccine immunity, which is not the same immunologically, as natural immunity. One of the major differences in the vaccine-induced immunity is that it cannot be passed from mother to infant. 

Since most vaccines are delivered by injection, the mucous membranes are bypassed and thus blood antibodies are produced but not mucosal antibodies. Mucosal exposure is what contributes to the production of antibodies in the mammary gland. A child’s exposure to the virus while being breastfed by a naturally immune mother would lead to an asymptomatic infection that results in long-term immunity to that virus. Vaccinated mothers have lower levels of virus-specific antibodies in the serum and milk compared to naturally immune mothers and thus their infants are unprotected.