"I eat fish."
This probably has more to do with the choice of English plurals for “fish”. My guess is that Ithim éisc. would be more likely to be translated as “I eat (multiple specific) fishes.” than as “I eat (multiple generic) fish.”, and that the English-to-Irish translation direction prefers the generic definition in lieu of any context.
Dinneen’s dictionary shows that before the spelling reform, iasc could be used for both nominative singular and nominative plural (the latter in addition to éisc). There was also a distinctive plural iascanna for multiple specific fishes. In the case of the traditional song Báidín Fheilimí, iasc was undoubtedly multiple generic fish.
ithim is the synthetic form of
itheann mé, which means "I eat". "He eats" would be
é is "he/him/it" but only when used with the copular
is as in "is fear é", which means "he is a man".
I eat fish = itheann mé iasc ; ithim iasc
He eats fish = itheann sé iasc
Normally, Irish is Verb-Subject-Object. "Eats he fish." Only with the
is construction is it Verb-Complement-Subject (or Verb-Comment-Topic). "Is (a) man he."
It's the synthetic form, which can be thought of as more like a conjugation than a contraction, even though they're not the same thing.
Long story short, in pro-drop languages like Spanish, the subject pronoun is optional. With synthetic verb forms, the subject pronoun is incorporated and precludes the use of the subject pronoun.