What was the origin of the custom of Catholics not eating meat on Fridays, and what is its theological significance?
There’s some discussion of this question here: Eating capybaras on Fridays
Q. What meat do priests eat on Fridays?
A. Nun.
It’s a later (last few hundred years) relaxation of the earlier practice, still done by the Eastern Orthodox, of abstaining from meat, milk, and (in the east) fish, wine, and oil on Wednesdays and Fridays, and fasting until the 9th hour, or about 3 in the afternoon. The command to do so is found in some of the earliest canons:
Its origins are probably in the Jewish practice of the time of fasting twice a week, but the later explanation given for it was that Wednesday is the day Christ was betrayed, and Friday is when He was crucified.
Catholics (and other Christian denominations) fast and abstain during Lent as a symbol of sacrifice as a reflection of the sacrifice Christ made. It’s also to bring the season of repentance into more focus.
And in reality, it’s kind of making a virtue out of a necessity.
In Medieval times, by Lent, there simply wasn’t enough meat left for the common people to eat it more than once a week. (Sunday is not a fast day during Lent; that’s how it adds up to 40 days.)
Their storage methods, and general economic situation, was such that meat was rare & expensive at that time of the year. Most meat animals had been slaughtered by then, since there was a limited supply of animal feed, and stables. It had to be reserved for the working animals (horses & oxen) and the pregnant females needed to produce next years’ herds. Only the prime breeding male (bull, boar, etc.) was likely to be kept over the winter – lesser males got slaughtered. In some species (like sheep & goats), where a spring-born male was of breeding age by fall, they might not keep any males at all, if it was a bad winter.
So there was a real practical reason to this religious practice.