You were not incorrect when you called the potato a vegetable. What is a vegetable? Vegetable means the edible part of a plant: what is a tuber? An edible part of the potato plant. Using the term vegetable to refer to things like tomatoes, pumpkin, potatoes may upset pseudo-purists, but it is not wrong; if you really want to be a purist, then you must almost omit the word “vegetable” near to (and I do say near to) completely, and refer to everything definitively (legumes, tubers, leaves...). It’s not necessary in casual conversation—such as asking people what their favorite potato preparation is (in some cases, it’s even going too far). Those who try to correct where nothing is wrong are pompous and are only trying to draw attention to their own (presumably superior) intellect. It’s fine to learn that potatoes are tubers, but they are vegetables. You are not a botanical scientist: don’t change yourself because you didn’t play by their rules.
All that being said, of course, makes me hypocritical. So what? I’m no better than them, and I can accept that. It’s you who I am trying to help here, not me.