There’s an argument for supporting public breastfeeding (that is, for not pushing nursing mothers to cover up while they’re nursing in parks, restaurants, offices, etc…) that claims, essentially, that breastfeeding is a natural act and that is why it should be permitted or even encouraged.
There’s a lot riding on that word, “natural”, and it’s a bit of a mischaracterization of the argument to reduce it to a single word and its implication. But anti-breastfeeding folks do tend to play on this implication, and they offer an argument against public breastfeeding that is supposed to be a reductio ad absurdum. A reductio is a style of argument in which the implications of your opponent’s claim are made explicit, and in doing so one or more of those implications are shown to be unsupportable and therefore one or more of the premises supporting the original claim must also be unsupportable. The reductio offered against public breastfeeding tends to go as follows:
1) Breastfeeding is a natural act.
2) Supporters of breastfeeding rely on the “naturalness” of breastfeeding to support the conclusion that breastfeeding ought to be permitted or encouraged in public spaces.
3) If “naturalness” is doing all of the work to get them the “public breastfeeding is okay” conclusion, then it ought to be enough to reach a bunch of other “public Natural Act X is okay” conclusions.
4) Urination, defecation, masturbation, sexual intercourse, oral sex, and expectoration are all natural acts.
5) Since these are all natural acts they ought to be permitted or encouraged in public.
6) It’s ridiculous to hold (5) to be true.
7) Therefore, the premise that forces the conclusion in (5), that somehow naturalness gets the “public breastfeeding is okay” conclusion, is false.
8) Therefore advocates of public breastfeeding cannot rely on naturalness to argue for public breastfeeding.
Leaving aside the question of whether or not breastfeeding advocates are relying as heavily on “naturalness” as is required to make the reductio work against them, there is still another problem with this argument: it commits the fallacy of equivocation.
The fallacy of equivocation is the use of a single term with more than one meaning to imply that something holding true of things connected with one meaning are also true of things connected with the other meaning. For instance, in the argument
1) All men are pigs.
2) Pigs root in the mud.
3) Therefore all men root in the mud.
there is an equivocation on “pig”. Although the argument looks valid (it has the form of a valid argument), it is obviously not, and the reason it doesn’t work is because of the equivocation. In one sense “pig” means “promiscuous or vulgar” and it’s a term of denigration. In another sense “pig” means “mammal with a snout and curly tail”. Claims about things that are connected to the term “pig” in one sense are not automatically true about things that are connected to the term in the other sense. Assuming so is an equivocation, and it’s a flaw in reasoning.
The equivocation in the anti-breastfeeding argument is on “natural”. Holding breastfeeding to be natural at all is not to hold it to be natural in the sense that every natural act is natural. Some acts are naturally sexual; some acts are naturally consumptive; some acts are naturally eliminative. They all share “naturalness” without exhausting “naturalness”, so there’s no necessary overlap in the concepts. To note that we would never permit naturally eliminative or sexual acts in a restaurant has no implications at all for the question of whether or not we should permit some naturally consumptive acts (eating with your hands) and not others (nursing).
There might be other reasons for not permitting public breastfeeding, just as there might be other arguments for public breastfeeding that don’t rely as much on the “naturalness” claim as the reductio makes it seem. But in any case the reductio itself does not work. Public breastfeeding cannot be challenged based on the fact that we ban other natural acts in public.