Why do people run 23/25 combos or 20/23 combos in front and rear.

What's the point as opposed to 23/23 or 25/25?

Anyone got some proof that this even matters?

My rodie has 23's front and rear. I don't know why a roadie would run a narower tire in the front, but I'm guessing it's faster due to less rolling restince and more arrowdynamic.
But I can tell ya that MTB run a wider front for stabulity reasons

I don't run it (23s front and rear), but the logic I see is that more of your weight is on the rear tire, and therefore more air volume in the rear makes sense. Less weight on the front, combined with the increased effect of aerodynamics, makes a narrow tire appropriate for that end.

For a minute there, I thought that you meant that your privates were getting smaller while your a$$ was getting bigger.

65% of your weight is on the rear tire. Putting a larger tire on the rear makes both tires equally "pinch flat" resistant. Sometimes, on a training ride, people in a pack do not call out (or steer around) pot holes.

yeah, a few guys at my club have tried it... since the rims are typically 19mm wide, it makes sense to have a 21mm max front tire and stick w/ a 23mm rear for the reasons sighted (21s ride harsh and its the rear that matter)...

some liked it, others found em harsh and prone to flatting...

I do something like that on my TT bike.. but that's because I opt for a super aero tubular front. It's probably worth some decent seconds over a 40k TT.

the wider rear tire will run at a lower pressure and provide the increased pinch flat protection and a more comfortable ride.

it makes sense to have a 21mm max front tire

No it doesn't. Cornering on a 21 is a serious PITA.

I did it when I went from 25's to 28's. I replace tires one at a time, and the rear tire wore out before the front. I replaced the rear with a 28 but kept the 25 on the front. I couldn't tell any significant difference.