Is there any halachic concern with breastfeeding on Shabbat? I believe the Chazon Ish brought down one can’t milk a cow on shabbos (which I disagree with personally), but under his logic would a similar issue present itself with breastfeeding from a human mother? I know technically, babies are not obligated to keep Shabbat, but would this be an issue of lifne iver on the mother’s part (at least according to the logic of the Chazon Ish)?
Admur 328:41 (ff.) rule that it is allowed.
It is permitted without restriction for a woman to breast-feed a child on Shabbos, even if the child does not need to breast-feed such as if he is already satiated, or has formula or other foods available. (see here).
The reason for this is because it is considered "Derech Achila" (See Shulchan Shlomo 328:56 in name of Rav SZ”A; Piskeiy Teshuvos 330:1).
However, it is forbidden to squeeze the milk into a vessel. Pumping extra milk is forbidden (Orach Chaim 328:34 ff.), due to the prohibition of melacha mefarek..
So to summarise:
According to Ashkenazim, it is only permissible to nurse on Shabbat if the infant feeds directly from the mother. A nursing mother who is experiencing pain may express excess milk if it goes directly to waste and is not collected in a cup or container.
According to Sephardim, a woman who is nursing and the baby doesn't want to nurse, to avoid a lot of discomfort it is permissible to express the milk but it should go to waste immediately, such as nursing into a disgusting cup or onto the ground.