Q:

Why is the word watch pronounced differently from words like patch, latch, match, catch, and batch?

Why doesn't watch rhyme with catch, batch, latch, patch, and match?

A:

Because of the rounded lips of the preceding consonant "w".
Many (but not all) English words with an "a" following "w", "wh" or "qu" have a different vowel from similar words with a different consonant.
So

what vs. that
watch vs. catch
squash, wash, vs. cash
war, warm vs car, arm

The exceptions often have a velar (/k/, /g/, or /ŋ/) or /m/ following the "a":

wag, whack, quack, wangle, swam, wham have the vowel of tag, tack, tangle, tram  not the vowel of wad, what, quad, wan.

But there are exceptions to this rule as well:

Quag has the vowel of quad despite its velar; and warm, swarm have the vowel of war, not that of harm.

