You are quite right about no Biblical basis for Abstinence from meat. But there is a part of the Catholic teaching that comes from Tradition (capital T). And it was Tradition (capital T) that gave us the books of the Bible in the first place. Read tonight's post for part 2.
Regardless of where you stand on Bible-only or Bible + Tradition + the magesterium (or teaching authority of the Church) the back story of "why fish on Friday" is history.
The part I mentioned about the people condemned to Hell for eating fish on Friday is only one-half of an old joke. 846 days ago