Too many educators, and students I encounter say “just flip the fraction” and do not know why or the reason for it.
I think algorithms are so baked into traditional math thinking that teachers can follow the traditions without realizing the self-limiting behavior. Also, the demands on teachers are so great that time for reflection or to ask “does this make sense?” can be limited. That’s why I have the utmost respect for the teachers who wrestle with these issues on Twitter, even if I don’t always agree with their conclusions.
What I like about Liping’s explanation is that it draws out the idea of multiplying by 1, expressed as a fraction, to create understanding of why you “flip” the second fraction.