it was the simplest way to map 3 letters to each number 1-9 on the keypad.[1] that way you didn't have a few numbers with 4 letters and had a consistent model.
[1] my grandfather explained it this way back in the early '80s. I couldn't find a good link to a more official source.
Except that 3 * 9 = 27, and there are only 26 letters in the English alphabet. They are actually mapped to the numbers 2-9, which leaves the question of why they didn't use 1.
The local prefixes of phone numbers don't/couldn't start with 1. If you map ABC to 1, you can't use those letters as the start of a word. (Your number could be GET-SOME but not AND-MORE.) This is because when you dial without an area code, your leading 1 would be interpreted as a long distance call. This is the same reason they didn't use 0, as that's the start of an international call (011).