Apparently fish aren't animals. :)
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But the fish / meat / etc is a tradition thing, so it comes from the culture surrounding the Christian, and probably more relating to Jewish history more than anything
During lent, you weren't supposed to eat meat as part of your fast. However, not eating meat is... not as enjoyable as eating meat, so they basically declared that fish doesn't count as meat so they could eat it without breaking the fast.
For similar reasons, they also declared beavers to be fish later on.