Rabbit trail: IMHO "perfect" doesn't mean "mature" since the verse reads "Perfect as…" Perfect as what? Perfect as our Father in Heaven. I love it when people take off on how we need to take the Bible at face value—"It says what it says" kind of stuff. Then they don't.
Well, about that verse, "It says what it says." It means to be as perfect as our Father in heaven is perfect. And the reasonable response is, "That's impossible!" And it totally is impossible. Picking up one of Jesus' similar discussions, what is impossible for man, is possible for God.
You see, the synoptic gospels (excluding John) were written TO THE JEWS, to the children of Israel. Not to Gentiles. Recall Jesus and the Gentile Syro-phoenician mother, pleading for her child's deliverance. Jesus spoke rudely, even harshly to her, asking what in the world did he have to do with Gentiles since he'd only been sent to the children of Israel? She flung herself at his feet (which not only indicated humility but ignored sexual conventions) and plead for her daughter: "But even the puppies under the table get to eat the crumbs" and Jesus delivered her daughter from that moment. And at another time when the disciples excitedly brought news that a group of Gentiles wished to speak with him, he refused. He had only been sent to the Jews. The first three gospels, recounting Jesus' ministry, were written for the Jews primarily and we have to be cautious about deriving theology from the synoptic gospels. We have to ask, of any text, did this have primary meaning for the Jews before casually adopting it into our theologies.
Jesus intended for the Jews to feel hopeless at the preaching of the Sermon on the Mount because he wanted to show to them that their religion—Judaism—was bankrupt and could bring no man into God's pleasure. Jesus was preparing the way for people to reject Judaism and accept him as the Messiah, and he would show them a better way—the way of salvation by grace. In this, he was laying the groundwork for the later ministry of Paul, as well as ushering into the world the Kingdom of Heaven which Paul also would flesh out in his day.
Conclusion: Jesus meant exactly what he said in order to produce despair in the hearts of his listeners, enabling or encouraging them to turn from the bankrupt Judaism to follow him as Messiah and on into the Kingdom of God by grace alone.