why do ants produce formic acid?

Answer 1

For the same reason that goats produce caproic acid.

[This is not a question about Chemistry.  It needs moving to Biology.]

Answer 2

The answer is dead simple.

For protection.

Answer 3

Because what other acid would they produce? The word "formic" is derived from the Latin word "formica," meaning "ant." I mean, it would be awfully strange for elephants to produce formic acid, what with them NOT being ants.