The five types of animals that could be brought as sacrifices were cattle, goats, sheep, pigeons, and doves. Fish are not brought as sacrifices.
Spiritual Walking, Flying, and Swimming
וְאִם מִן הָעוֹף עֹלָה קָרְבָּנוֹ לַה' וגו': (ויקרא א:יד)
[G‑d told Moses,] “If someone’s sacrifice to G‑d is an ascent-offering of fowl.” Leviticus 1:14

Mammals allude to those among us whose animal nature is relatively pronounced. Fowl, because they can fly, allude to those of us who are less “earth-bound,” i.e., who live a more intellectual life and can therefore “fly” above a purely animal existence. Nonetheless, just as fowl need to periodically rest from flight, human intellect is limited by nature. Therefore, fowl, like mammals, are used as sacrifices, since both our animal natures and our intellects need to be spiritually refined and uplifted.

In contrast, fish, which must remain constantly in water, allude to those of us who have so refined themselves that they remain always connected to G‑d, “swimming” constantly in Divine consciousness. Since the Divine side of our personality does not need the elevation that our animal side does, fish are not used for sacrifices.1