Let me suggest to you an alternative reading.
Much of Jesus' teachings on the Sermon of the Mount represent a point of view quite similar to the rabbis (the Pharisees) of his generation as reflected in their teachings recorded later in the Mishna and the Tosefta and in the teachings of the Hebrew Scriptures. This point of view can be supported by Jesus' own words where he says in Matthew 5:17-20:
17 “Do not think that I have come to abolish the law or the prophets; I have come not to abolish but to fulfill. 18 For truly I tell you, until heaven and earth pass away, not one letter,[c] not one stroke of a letter, will pass from the law until all is accomplished. 19 Therefore, whoever breaks[d] one of the least of these commandments, and teaches others to do the same, will be called least in the kingdom of heaven; but whoever does them and teaches them will be called great in the kingdom of heaven. 20 For I tell you, unless your righteousness exceeds that of the scribes and Pharisees, you will never enter the kingdom of heaven.
See also Matthew 23:2-3 ("The scribes and the Pharisees sit in the seat of Moses; therefore all they tell you, do and observe....").
Taken at its face, Jesus wants his followers to observe Torah exactly as the Pharisees were teaching and as opposed to the teachings of the Sadduccees (who at the time had one of its own as the High Priest, and who rejected the concept of life after death and punishment for sins after death, concepts which the Pharisees supported).
The rabbis taught that a person should strive to observe the 613 Torah commandments (365 negative commandments -- i.e. "thou shalt not..." and 248 positive commandments, i.e. "thou shalt..."). They would see little difference between Jesus' advice to be perfect on account that God is perfect. This parallels the teaching of Leviticus 19:2-3 where God tells Moses to tell the Jews, "You shall be holy kedoshim because "I the Lord your God am holy." The rabbis would only have said that the use of the word "perfect" for "holy" is a translation error. Being holy, or kodesh, is not a matter of being "perfect" per se. It is a striving to sanctify oneself to God. The same root is used for the word for the marriage ceremony, kidushin where the husband wife sanctify themselves to each other to the exclusion of everyone else. Many of the commandments regarding our relationship with God -- e.g. keeping kosher, observing the Sabbath, prayer, laws of ritual purity -- are designed to make us more sanctified to God and divorced from secularism.
Deuteronomy 30:15-20 also lays out the importance of God of obedience to His commandments:
15 See, I have set before you today life and prosperity, death and adversity. 16 If you obey the commandments of the Lord your God[a] that I am commanding you today, by loving the Lord your God, walking in his ways, and observing his commandments, decrees, and ordinances, then you shall live and become numerous, and the Lord your God will bless you in the land that you are entering to possess. 17 But if your heart turns away and you do not hear, but are led astray to bow down to other gods and serve them, 18 I declare to you today that you shall perish; you shall not live long in the land that you are crossing the Jordan to enter and possess. 19 I call heaven and earth to witness against you today that I have set before you life and death, blessings and curses. Choose life so that you and your descendants may live, 20 loving the Lord your God, obeying him, and holding fast to him; for that means life to you and length of days, so that you may live in the land that the Lord swore to give to your ancestors, to Abraham, to Isaac, and to Jacob.
Although these verses assert God desire that the Jewish people follow God's commandments, it does not speak of perfection. The prophets did not see perfection in Torah observance as a requirement for righteousness because a lifetime of perfect observance is an impossibility. King Solomon, writing in Ecclesiastes 7:20, states "For there is not a righteous man upon earth that does good and does not sin." King David, writing in Psalm 19:8-14, praises God as perfect, the Torah laws as correct, enlightening and true, but notes that if he were judged on sins he was unaware of, he could never achieve "perfection." Accordingly, he asks God to help him to avoid sinning intentionally and to forgive and overlook his hidden sins, so that "then I will be perfect and I will be cleansed of much transgression."
This and much of Jesus' teachings on the Sermon on the Mount contradict the writings of later church leaders who questioned the point of observing the commandments at all, placing faith over actions. But if you look at Jesus as a rabbi of his era, this verse in Matthew is not complicated at all. I think he and the rabbis would agree that man's goal should be to reach perfection, and we should never cease pursuing that goal.