The pairing logic, in depth
Pizza is deceptively hard to pair because three things fight at once: acid from the tomato, salt and fat from the cheese, and bitter char from the crust. Acidity is the lever that solves all three. A wine that matches or exceeds the sauce's acidity stays bright in your mouth; a low-acid wine tastes flabby and sweet the moment tomato hits it. That's the whole reason Italian reds - grown alongside this food for centuries - are the default: Sangiovese, the grape of Chianti, is naturally high-acid and savory.
Tannin is the trap. Big Cabernet and Brunello have grip that's lovely with a steak's protein, but tomato acidity strips the fruit off tannin and leaves a metallic, drying finish. Keep tannin in the medium range so it has something to do (cut the cheese fat) without dominating. Body should track the topping: a plain Margherita wants a lighter pour, a meat-lover's pie can take a fuller Zinfandel or Shiraz.
The biggest mistake is pairing to the topping instead of the sauce. A white pizza - no tomato, just cream, garlic, and cheese - flips the whole equation: now there's no acid to match, so a red tastes heavy and a crisp white or dry rosé is the right answer. Likewise a sweet BBQ-chicken pie wants a hair of sweetness in the glass (off-dry Riesling) to keep the sauce from making a dry wine taste sour.
Serve reds slightly cool - 60-65°F, about 20 minutes out of the fridge. Pizza is casual, fast, and a little greasy; a cool, juicy red is more refreshing than a warm, heavy one. None of this requires an expensive bottle. The acid-and-fruit profile that pizza wants is exactly what inexpensive Chianti and Côtes du Rhône deliver best.