New Wine in New Wineskins

Then John’s disciples came and asked him, “How is it that we and the Pharisees fast often, but your disciples do not fast?”

Jesus answered, “How can the guests of the bridegroom mourn while he is with them? The time will come when the bridegroom will be taken from them; then they will fast. No one sews a patch of unshrunk cloth on an old garment, for the patch will pull away from the garment, making the tear worse. Neither do people pour new wine into old wineskins. If they do, the skins will burst; the wine will run out and the wineskins will be ruined. No, they pour new wine into new wineskins, and both are preserved.”
(Matthew 9:14-17, NIV)

I used to read this and wonder what is Jesus talking about? I mean, I get the fasting vs. celebrating, but what does he mean about the patch and wineskins. I didn't get it, but now it seems so simple. You don't mix the old with the new. Who in Jesus' day would do such things that were against the common sense of the day?

Take a second look, the old cannot handle the new. The old, threadbare cloth tears, the old, brittle wineskins split. You can't take your old way of thinking about God, yourself, others, the cross, and salvation, sprinkle on a little grace and end up with a new way to follow the old doctrines of self-justification and self-promotion. It just doesn't work.

So from now on we regard no one from a worldly point of view. Though we once regarded Christ in this way, we do so no longer. Therefore, if anyone is in Christ, the new creation has come: The old has gone, the new is here!
(2 Cor 5:16-17, NIV)