If you DON’T change the filter every time you change the oil, there’s little point in changing the oil, as the filter holds all the crap that the oil has picked up during its use, and you’re basically just holding a quart of FILTHY oil in the system, negating the clean oil you just bought.
It’s like keeping 1/4 of last night’s dishwater to wash tonight’s dishes.
That simply isn't true. The contaminants are captured in the filter and stay there unless the filter fails. I myself use $12 K&N oil filters and generally change them on every second oil change. The oil doesn't look dark even after 5,000 miles. The cheap filters I wouldn't trust for even one oil change; the chance of an internal tear is too high.
It’s like keeping 1/4 of last night’s dishwater to wash tonight’s dishes.
That's a false analogy because the contaminants don't circulate through the system. I periodically send an oil sample to an analysis service and it always looks good.