Pope Paul VI kept Friday as a day of penance but dropped the abstinence of meat under penalty of sin. What actually happened is that Catholics heard the part about not abstaining from meat and were deaf to the rest of the message emphasizing Friday as a day for us to continue to do penance.
Friday abstinence was part of our identity as Catholics and an outward sign of our faith. It was identifiable to the public much like ashes on Ash Wednesday. Cardinal Dolan refers to sociologists that warn the Church of losing these external markers. These outward public signs orient us toward our membership in the Church; we are part of something meaningful and larger than ourselves, the Body of Christ.
Racco Palmo has posted the audio of Cardinal Dolan's interview on Sirius Radio following his address on this topic.
Cardinal Dolan's Presidential Address to the USCCB