Some of the antibodies in breastmilk are stimulated by the act of baby s mouth on the breast- the antigen that is in baby s saliva is transferred to mum while feeding and mum in turn produces antibodies in the milk that will fight off infection.

Young babies also get benefit from being exposed to parental flora (bugs on mum s skin) and this would occur during direct breastfeeding. I'm not sure how relevant this is in older babies.

using bottles takes away from the sterility of just going from breast to baby.

stimulation by pump can be less effective than baby sucking.

when feeding by bottle, it is possible that baby s ability to self regulate amount they need to drink will be overridden by carer, and the baby take in more than they want/need.

more work for mum