Precisely what does "meatless Fridays" have to do with the teachings of Christ?
sacrifice
"At the heart of all penance is the call to conversion. Jesus' imperative "Repent, and believe in the gospel" (Mk 1:15) makes explicit this connection between authentic discipleship and penitential discipline. Discipleship, our following of Jesus, embraces discipline, a firm commitment to do whatever is demanded in furthering God's kingdom. Viewed in this way, the virtue of penance is not optional, just as weeding a garden is not optional for a responsible caretaker. The gardener is concerned with a bountiful harvest; the disciple is concerned about greater conformity to the person of Jesus.
If we are serious about embracing the penitential discipline that is rooted in the call to discipleship, then we will identify specific times and places for prayer, penance, and works of charity. Growth in spiritual maturity demands a certain level of specificity, for it shows that we take seriously God's call to discipline and are willing to hold ourselves accountable. In our Catholic tradition we specify certain days and seasons for special works of penance: Fridays, on which we commemorate the death of the Lord, and Lent, our forty days of preparation for the Easter mysteries."
It's a form of fasting. (A very wimpy, watered-down, and easy-to-observe form of fasting, but a form of fasting nevertheless.)
Christians have fasted since the earliest days. Christ commends "prayer and fasting" to drive out demons, and himself fasted in the desert for 40 days at the beginning of his public ministry. The Didache (ca. AD 80) commands fasting on Wednesdays and Fridays. Fasting is a form of self-denial and mortification. There are whole books written on fasting and other spiritual disciplines. A simple explanation of "why should I fast" is that, by fasting, you voluntarily give up some created natural good to remind yourself to focus on supernatural goods: God and intimacy with him through grace.
We are imitating the Master - remember when he went to the desert and fasted? It is a small way to imitate him and by so doing remember the redemption he purchased for us so that we might be inspired to lead lives in accord with the abundant grace bestowed upon us.
I think your question is disingenuous. You could have figured the answer to your question quite easily on your own.
Good question. Here's the closest I can find:
Now the Spirit manifestly saith that in the last times some shall depart from the faith, giving heed to spirits of error and doctrines of devils, speaking lies in hypocrisy and having their conscience seared, forbidding to marry, to abstain from meats, which God hath created to be received with thanksgiving by the faithful and by them that have known the truth. -- I Timothy 4:1-3
Its a part of fasting. Aside from giving up a quantity of food in fasting, you also give up luxurious foods (meat, eggs, cheese, etc.)
"And the disiples of John and the Pharisees used to fast; and they come and say to him: Why do the disciples of John and of the Pharisees fast; but thy disciples do not fast? And Jesus saith to them: Can the children of the marriage fast, as long as the bridegroom is with them? As long as they have the bridegroom with them, they cannot fast. But the days will come when the bridegroom shall be taken away from them; and then they shall fast in those days." (St. Mark 2.18-20)
He established the Catholic Church to teach in His name
Our Lord was crucified on a Friday. To remember and honor His ultimate and perfect sacrifice, we are reminded by the Church He founded to do this small penance weekly. This weekly reminder that it was OUR SIN that crucified Our Lord is there to help us on our path to sanctity. Our Lord encourages us to "Go and SIN NO MORE". We ought to listen to Him, don't you think?