Why it is not recommended to mix the milk of different days?
Even when kept refrigerated, milk gradually spoils due to micro organisms. In case the first day's milk was on the threshold of spoiling, you are effectively bringing the third days milk also to that condition by mixing it with the first day's milk (which by now may have significant amount of microorganisms).
First day's milk bottle/vessel might have been retrived from the fridge, opened, and kept at room temperature (very short durations), and kept back multiple times by the time the third day's milk arrives. This gives microorganisms opportunity to enter and multiply even if the original milk was Pasteurized and sealed airtight in a sterile packaging.
In fact, curd is propagated by mixing fresh milk with leftover curd. Same with sourdough starter.