The association isn't new, see the related slur for gay people.
1. it's unfair that boys who chose to play flute got bullied for it
2. it's not good that his brother essentially took his choice from playing flute by reinforcing #1
3. #2 is actually simultaneously the way to minimize the negative effects of the authors choice of instruments
So in spite of those first two things individually being pretty shitty, they actually give you an optimal outcome (socially) in school. Ideally we get to a place where #1 stops happening, but you won't solve it by going against the grain, you'll just be a martyr for nothing.
The author got grief for playing the clarinet too, and from poking around at their other articles I think they'd have had a lousy time regardless of what instruments they might have chosen, if he hadn't got bullied about the flute he'd have gotten bullied about something else.