Why does English say 'father' where Latin says 'pater'?

English says 'father' where Latin says 'pater' because, in the first millennium BCE, the ancestor of the Germanic languages reshuffled its consonants in a regular pattern now called Grimm's law. The old Indo-European word kept its p in Latin pater, Greek patēr and Sanskrit pitr, but in Germanic every such p became f: Gothic fadar, English father, German Vater. It wasn't one word changing on a whim. The same shift turned d into t, which is why Latin decem matches English ten.

The law works like a game of musical chairs. Old p, t, k became fricatives such as f; old b, d, g slid into the empty seats as p, t, k; and the breathy bʰ, dʰ, gʰ became plain b, d, g. That is why scholars saw, for the first time, that sound change is systematic rather than accidental.

The pattern was first noticed by Friedrich von Schlegel in 1806 and worked out by the Danish scholar Rasmus Rask in 1818, but it is named after Jacob Grimm, who set it out in 1822 and who also edited Grimms' Fairy Tales with his brother Wilhelm.

Grimm saw that many words broke his rule, and 'father' is one of them. The puzzle lasted decades, until the Danish linguist Karl Verner noticed that the exceptions depended on where the stress fell in the ancient word. He explained it first in a long personal letter to a friend, in 1875.