Why can't you eat meat on Fridays during Lent?

I'm sorry to have to contradict most of the answers so far except for Singwell's. As to the rest of the points of confusion:

1. It has nothing to do with what Jesus did, or did not, eat at the Last Supper.

2. It IS on Fridays because of the belief that Jesus was executed on a Friday. However, in earlier times, meat was forbidden all through Lent, not just on Fridays.

3. It IS a sacrifice Catholics are required to make to honor Jesus' sacrifice of his life.

4. It WAS mandatory for Roman Catholics every Friday all year until the Vatican II conference led to many changes in Catholic rules; NOW it is only mandatory on Fridays during Lent.

5. Lent is the roughly 40-day preceding Easter (actually 43.5, see #6 below). It is a time when Catholics are supposed to consider the sacrifice Jesus made for humanity's sins, consider their own sins, and make some sacrifice of their own, see below.

6. Because people are so confused about the length of Lent, here is an answer from Father Larry Rice, head of the Newman Center for Catholics for the University of Ohio at Columbus: ----"Lent is 43.5 days long, and is the same every year. The date for Ash Wednesday is determined by the date for Easter, which moves (First Sunday after the first full moon after the vernal equinox). Lent ends with the Mass of the Lord's Supper on Holy Thursday, making it a total of 43.5 days long. Every year people ask me if Sundays are part of Lent. The answer is yes."---- There you have it from a Roman Catholic priest regarding modern rules. To help you get oriented to the explanation, Holy Thursday is the day before Good Friday; Good Friday is two days from Easter Sunday. Therefore, Easter Sunday doesn't count as part of Lent, which may have led to the confusion about whether Sundays count at all. Wikipedia gives the wrong answer about whether the other Sundays count; see Father Rice's explanation above. Eastern Orthodox Catholics used to excuse Saturdays as well as Sundays from Lenten fasting; Roman Catholics sometimes were excused on Sundays (after Mass).

7. The sacrifice Catholics make can be something like cigarettes or food or video gaming; or a favorite toy or habit; or something like watching a particular television program. It is supposed to be something that they enjoy and will really miss, that will remind them of how hard it was for Jesus to give up his life if they are having a hard time giving up chocolate.

8. The Lenten restriction on meat came out of the Middle Ages, when the Church declared fasts in honor of all sorts of events (certain saint's days, or in honor of a day of prayer for success in war, or in mitigation of sin for the whole town). These fasts were declared for religious reasons or for political reasons (the health of the queen, luck in war, etc.) but the underlying reason was, most fasts were declared to try to make the winter food supply stretch until spring. Remember, in the Middle Ages, there were no grocery stores. Whatever had come in at harvest was all everyone in town had to eat until the next year. Enforced fasts were a way of stretching the food supply out a little longer, and preventing people from eating up the livestock they would need the next year, and eating up the seed they would need for planting in the Spring. Remember, meat used to be banned for ALL of Lent, not just Fridays, so this was an effective way of protecting the food supplies at the end of winter. See any of the books of anthropologist Marvin Harris for more on the social usefulness of fasting customs.

9. The prohibition on meat includes white meat and red meat, including chicken. Fish and seafood were permitted, but unless your community was on a coast, you'd usually have some kind of a cheese dish, if you were lucky. At some times and in some places, a bishop might lift the prohibition on chickens and other fowl; but usually, bird meat was treated like other meats, and forbidden.

10. There are two odd exceptions to this: at one point, Church authorities declared beaver meat could be considered fish; and there was a similar situation with the South American semi-aquatic mammal known as the capybara, which was also declared a "fish" for the purposes of Lent because it lived mostly in the water. Note that neither beavers nor capybara are domestic animals -- eating them wouldn't cut into the core livestock needed to maintain farms in the Spring, see #8. LATE ADDITION: Another similar example: I just learned that muskrat also was a permitted "fish" in some Canadian/Northern U.S. regions, see http://www.freerepublic.com/focus/f-religion/1797624/posts
and this fellow claims that sea turtles and iguanas are also permitted:
http://www.opinionjournal.com/taste/?id=110008041
Elsewhere, I saw references to intermittent declarations that seabirds could qualify as "fish," but I didn't find a source I considered reliable or specific enough about that.

11. Compare Lent to Ramadan for an interesting contrast in fasting customs. Note that they are both roughly a month long (28 days of Ramadan, 43.5 days for Lent). Both depend on a lunar cycle.

12. Mardi Gras, which means Fat Tuesday, got that name because in some regions of Europe at some times in the Middle Ages, it wasn't just meat that was forbidden during Lent: it was other animal products like butter and eggs as well. So Fat Tuesday got its name from the pancakes and other cakes that were made then to use up the household's supply of eggs and butter before Lent started. Note: if people weren't eating the eggs, the hens would have hatched them out, thus increasing the supply of chickens and domestic ducks at the beginning of the farming year.

13. Fat Tuesday is usually called Shrove Tuesday in English. To be shriven (or shrived or shroved) means to go to Confession, and many people do that before Ash Wednesday, the beginning of Lent, to be cleansed of sin before the long period of Lenten contemplation, reflection, and sacrifice. It may have been mandatory at some point, I don't know. It may still be mandatory; I don't know that either. :)

There! A baker's dozen of Lenten trivia. :)