I'm not sure you're understanding how breastfeeding works. It protects rather than transmits.
A baby is born with a sterile gut (gastrointestinal tract). I'm sure you've heard of a sterile environment in a hospital? Because breastmilk is a physiological substance, like blood, when it enters the baby's gut, the baby's gut remains sterile. The breastmilk also helps to develop healthy flora in the GI tract and to seal it from harmful pathogens.
This is the case only while the baby is exclusively breastfed, and as long as nothing but breastmilk has entered the baby's gut. When even the smallest amount of anything else is introduced, such as formula or solid food, the flora of the baby's gut changes, and these gut changes make the baby more at risk for disease. This is the manner in which breastfeeding protects the baby from disease, by the maintenance of a healthy gut.
The good news is that the sterile gut can be regained after two weeks of exclusive breastfeeding in the case in which exclusive breastfeeding has been interrupted.
Breastfed babies can become ill though, even very ill, but are more likely to fend off illness because their physiologies has only been exposed to the milk of their own species.
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