Essentially, because bacteria like to eat lactose (milk sugar, not sweet like ordinary sugar but closely related chemically). The breakdown product is lactic acid, which is why sour milk tastes, well, sour. The acidity also makes the protein molecules in milk clump together, forming the solid lumps or curds.
If you control the curdling carefully, the result need not be nasty. Soft cheeses like cottage cheese are made by intentionally curdling milk.
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