"Just use a pump!"...
I love experts who know nothing about their subject, have no interest in learning anything about it, and yet want the right to sneer dismissively at people because they have the answers.
So, here's a few things.
One, breast pumps are expensive. Good ones cost about as much as your game console, and they require far more maintenance to use in a comfortable and sanitary fashion. Time and money. Which is one thing if, say, it's a matter of a working mother who needs nutrition to be available to her child while she's away; it's quite another if it's just the matter of offending the sensibilities of self-centered prudes who think the world caters to them, an outlook whose comparison to a nursing child seems more than slightly ironic.
Two, not every woman can use a breast pump. Expressing milk can be difficult. Some women have to take classes just to learn how to feed their child, and some end up giving up and using formula because they just can't do it. This is a good part of the reason groups like "La Leche League" exist. And if feeding a child from your body is hard, just try feeding a machine- the maternal feelings necessary can be rather difficult to summon.
Three, bottle feeding can be a lot more difficult than you would think. Milk has to be kept fresh, and then it usually needs to be warmed. Depending on the age of the child, you may need specific bottle tips to keep the fluid flowing at the right rate and prevent the child from taking in too much air. So there's a whole other set of gear... which could, again, be completely unnecessary if uncomfortable people who feel no one owes human infants any consideration since they aren't helpless crying infants anymore (more or less) could use their mighty neck muscles to turn their heads forty-five degrees.
In short, the ability to feed a child, including in public, is a basic function useful to the existence of the human race. The attitude that those performing such a simple act should bend over backwards to avoid offending you is something the human race is progressing beyond with or without you.