Like I said, this is clearly a mother thing, so I’ll just take a step back and let you have it your way.
But consider this: were a male to act in the manner you describe, fully covered by a partition / blanket / ect, he would be removed from the plane in handcuffs. And rightfully so.
Some things, regardless of how “right and within your rights” are still very much not ok to do. And yes, I / my wife travelled a great deal with infants. And yes, she nursed (but used a bottle as well. And never once did the nursing in public become an issue. There are always altenatives, if you feel like seeking them out.
(Note, I changed my call out from “this is a woman thing” to this is a mother thing, as from the feedback, it seems that most single women see this as out of bounds too)