You can have a house that's halfway through being built. And the work that's done so far can be flawless, with no problems anywhere, but it's still not a perfect house.
Or, likewise, have a look at Adam and Eve. They were created without sin, but when temptation came along, they chose to transgress God's commandments. Jesus, on the other hand, was also without sin, but he stayed that way even though he was tempted in all points, as we are..
This shows the difference between sinlessness and perfection: perfection implies a state of completeness, in which you no longer commit sin because you've matured beyond the point of yielding to temptation.
Jesus's atonement can take away our sins, making up for past wrongdoings in a way that we are incapable of. But when he commands us to be perfect, that calls for effort on our parts as well, to strive to live the Gospel, to work at improving ourselves until it becomes part of our nature.
Everyone has some sins that they just don't understand. Even if they can see how it might tempt some people, the idea of choosing to do it themselves just feels foreign to them. (Meanwhile, everyone has other sins that just feel natural and normal to them.) My understanding of perfection is that, when our faith and humility, repentance and obedience lead us to the point where every sin feels that foreign to us--which will most likely not be during this life--that that's the point at which the perfection that Christ commanded of us has been reached.