I can get behind calling it human milk because it’s weird how what we call “normal milk" is actually cow’s milk for cows.
But chest milk sounds … cutesy. Like they just wanted something to rhyme.
The only thing I would say both you and the hospital got wrong is thinking breasts and breast milk are exclusively feminine phenomenons. Men and women both have breasts and can lactate (and yes, even biological/cis men have breasts, can lactate, and get breast cancer). Every human being on the planet has breasts, and society really needs to stop sexualizing breasts and then we wouldn’t have this problem.