The pairing logic, in depth
The biggest myth in wine is “red wine and cheese.” It's true for some cheeses and a disaster for others. The reason is fat and tannin: many cheeses are soft, creamy, and high in fat, and fat plus tannin produces a chalky, bitter clash. That's why a runny brie or a fresh goat cheese tastes far better with a crisp white or Champagne than with a Cabernet. Red wine only shines with the cheeses that have enough dense protein - hard, aged ones - to bind and soften its tannin.
Think in two axes: intensity and texture. Intensity means a delicate cheese wants a delicate wine and a powerful cheese wants a powerful wine, so neither erases the other. Texture means fat needs to be cut - by acidity (a zippy Sauvignon Blanc or sparkling) or, for the saltiest cheeses, by sweetness. Get those two right and the specific grape matters less than you'd fear.
The blue-cheese rule is worth memorizing because it's counterintuitive and unbeatable: pungent, salty blue wants a sweet wine. Port with Stilton, Sauternes with Roquefort, an off-dry Riesling with Gorgonzola - the sweetness and the salt cancel each other into something richer than either alone. It's the clearest example of pairing by contrast rather than by similarity, and once you've tasted it you'll stop reaching for red with blue forever.
For a mixed cheese board - which is how cheese is actually eaten - you can't optimize for every wedge, so play the percentages. A high-acid white (Champagne, Sancerre, Riesling) is the single most board-friendly choice because it handles the soft and tangy cheeses that red ruins, and still does fine with the hard ones. If you want a red on the table for the cheddar and the aged Gouda, choose one that's fruit-forward and only moderately tannic so it doesn't bully the softer cheeses sharing the plate.