Jesus preached quite often of not clinging to the Old Testament, but rather they should listen to his teachings and parables today as the new word, come to fulfill the old word. The reading of the day comes from Matthew 9:14-15
Then the disciples of John came to Him, saying, "Why do we and the Pharisees fast often, but Your disciples do not fast?" And Jesus said to them, "Can the friends of the bridegroom mourn as long as the bridegroom is with them? But the days will come when the bridegroom will be taken away from them, and then they will fast"
Can you imagine the difficult time in which Jesus was preaching and the utter turmoil the people were dealing with. Occupation by the Roman forces, corruption and hypocrisy by the Pharisees and priests of the period. What an opportunity to strike out and say, that was the old ways and I have come with new ways. New ways of thinking, new ways of believing and new interpretations of the old law.
It took quite a bit of courage and fortitude to strike out and let his followers know that there will be time to fast, when I am gone and to follow the ways - but NOW, I want you to be with me and to be present with me while we break open the word.
The 'disciples' of John and the Pharisees followed the old ways and with it, appeared sullen and mournful during their fasting. Jesus is the living word of GOD and as such was the embodiment of love and joy and his declaration, although a foreboding of the future events, declared that when he was gone - there would be plenty of time to mourn.
This also hearkens back to the prior reading (see Day 1, Matthew 6:16), as Jesus said:
When you fast, do not look somber as the hypocrites do, for they disfigure their faces to show men they are fasting.
Again, as stated before, feel free to follow the old ways, but don't wear it on your sleeve like it is a garment. Don't display your fasting or your rituals - keep them internal and private between you and GOD - GOD sees all, knows all.
So the message is clear - Jesus brought something new and entirely different to the table of man. Our ways of thinking about our religion and our acts towards our fellow men, were about to be altered for the better. This almost sounds like an infomercial where Jesus was bringing about 'NEW' and 'FRESH' way of interacting with GOD. But the truth is, it was much different than the people of that period were used to experiencing.
So, feel free to follow the Old Testament, but prepare to LIVE in the NEW TESTAMENT. Listen to the words of Christ and open your ears and your hearts to his messages.