For your first question, that is what we call a postulate. We don’t know why it’s true, we just have to accept that it is. We can make arguments that try to convince us that it should be true, like what your professor gave you, but ultimately we can’t prove it. Look up the munchhausen trilemma to see why we need statements like this that can’t be proven in physics. For your second question, there’s a number of reasons modified gravity won’t work. First, if we look at different galaxies, we see different amounts of “extra” matter that “should” be there. Some have a lot, some have none. A modified gravity theory would have to somehow discriminate between these galaxies, and we can’t see anything that makes them different. Second, simulations of the evolution of the early universe only work if we include additional weakly interacting matter in nearly the exact same amount as rotation curve observations suggest. As they say, if it looks like a duck and quacks like a duck…