Agreed - in general you want to make cheese with the milk as fresh as possible. Assuming we're talking about milk stored in a refrigerator, be aware that cold storage of milk actually does some damage in terms of how it will work for making cheese. And the closer the milk gets to sour / clabber, the more you have an unknown mix of bacteria - not necessarily dangerous, but not necessarily the right flavors. (There are, of course, cheeses that are made using raw milk, allowed to clabber naturally - but this is done purposefully and in a single episode, not drawn-out over time in the fridge. And even then, most people will add at least some culture to the milk to make sure the desired bacteria dominate.)