Maybe it was taught in the wrong order. Matrix multiplication makes perfect sense if you see (a) that linear transformations can be represented as matrices, I.e A = f, B = g and (b) you define matrix multiplication so that the composition of linear transformations I.e. f(g(x)) = ABx gives the same result. That’s a pretty cool idea, that you can represent a function by a matrix and that you can compose those functions and the composition is the same as multiplying the matrices together. So let’s say f(x) computes the derivative of a polynomial, and you have a matrix representation for that, say A. Now what if I want the second derivative? That would be f(f(x)) or just AAx.
I suppose I would tell a student that asks “why would I want to remember the stupid rule for multiplying matrices together in that way?” to try and figure out a rule for multiplying two matrices together such that you could represent functional composition by it, and they would self-discover the matrix multiplication rule and see why it would be useful to do it that way.
It's not that it didn't make sense, it's that it was boring! Of what use is it? Sure, you have composition of linear transformations, but of what use is it again? If there's no use, it's boring. Pure math is like a puzzle, some people really love to solve the puzzle. The joy is in the solving the puzzle, and then for some people the joy only manifests if it's applied. Point of the original post being that math is harder for students to accept in its pure form if not applied.
I suppose I would tell a student that asks “why would I want to remember the stupid rule for multiplying matrices together in that way?” to try and figure out a rule for multiplying two matrices together such that you could represent functional composition by it, and they would self-discover the matrix multiplication rule and see why it would be useful to do it that way.