Breasts aren’t like peeing where there’s a bladder linked to a single tube that can be forced to let things through backwards. Milk production is anatomically very similar to sweating, where fluid generated in clusters of small glands soaks out through tiny pores in the surface. Imagine a part of your skin that gets sweaty, and pressing it up against your mouth trying to blow air back in through where you sweat. It just would not work out that way.

There are various types of technology in development for needle-free injection of drugs, and they work on principles of generating a lot of force in a tiny area to shove stuff past the outer layers of skin using more direct pressure than you could generate with your mouth and breath.