Jesus is drawing a contrast in ways of dealing with the Old Testament. Notice, by the way, what the contrast is not. Jesus does not contrast “to destroy” with “to maintain”—as if all continues as normal. Jesus well knows that much is changing; He comes as the Mediator of a new and different covenant. In the Sermon on the Mount itself, Jesus says new things far beyond the law’s own obvious intent (Matthew 5:31-42). No, Jesus does not choose mere maintenance. Rather, the contrast Jesus chooses to make in Matthew 5:17 is between pulling down and filling up.
Jesus came to fulfill, not destroy.
There is a great deal of difference between pulling down the Law as compared with filling up (fulfilling) the Law. Think about a contract—an agreement or covenant— between a house-builder and a customer. The builder respects the contract; he completes the house just as agreed. With the house built, the contract has been fulfilled. We would have no difficulty understanding the builder who says, “I didn’t come to tear down (abolish) this contract; I came to fulfill it.” In this sense, the fulfillment of a contract also means its conclusion. Since its conditions have been met, they are no longer binding.