I have no ethical reasons or other reasons for someone to avoid breast-feeding their child. I thought it was interesting though when someone once brought this up and said yes of course breast milk is vegan. I assumed the opposite: breast milk comes from an animal (humans are animals) and so it is of course not vegan! Now if we take the definition that eating vegan means avoiding all unethical animal products, then maybe breast milk is vegan. Let's think about it like this. If there were a magical land where chickens lived peacefully and happily and happened to lay their eggs, desert them and forget about them, would a human who used telekinesis to snatch this egg for her consumption be eating vegan?
I think the point of "going vegan" is that you don't have to think about whether the farm animal lived a happy life - if there is that chance that he didn't, you're not taking it. You're avoiding all animal products as best you can. So by that definition, I would say that a baby who drinks breast milk isn't consuming vegan food in that moment. Can they call themselves vegan if the rest of the baby food they eat is veggies? Sure, why not. Are they living ethically? They're eating ethically, from my point of view. They might be crying just to annoy their mother, though - that doesn't sound nice.