When Jesus taught in Matthew 5:48 "Be ye therefore perfect, even as your father which is in heaven is perfect," I think that it's interesting that He didn't tell us to be perfect like Him. Why is that? After all, He was perfect, wasn't He? Maybe perfection requires more than just an absence of sin and a multitude of good works, though.
The definition of the word perfect has changed some over the ages. The original meaning was that of being finished, completed, or even whole. I think this sheds some light on why Jesus would tell us to be perfect like His father, rather than like Him.
First, Heavenly Father is the finished, complete, and whole of perfection. He is the Father, the great Elohim, the Eternal God. Jesus, while also a God, was still on the earth, still in the midst of His mortal ministry, and as such couldn't have been said to have been finished. He still had work to do.
Second, and this may be a stretch for some, is that Heavenly Father is married. He is complete and whole because He has an eternal marriage partner. When Jesus taught about marriage, he said that "For this cause shall a man leave father and mother, and shall cleave to his wife; and they twain shall be one flesh." (Matthew 19:5) God instituted marriage from the beginning, and meant for it to be a way for a man and a woman to complete each other. Marriage was to take two halves and make a whole, hence the ability for two to become only one. The only way for two to be one mathematically is if the two are halves. And half of a person can never be whole, or perfect. This could mean that Jesus' teaching to be "perfect" also had application as a sermon on marriage.
The more that I read about marriage and its importance to our selves, families, and society, the more that I am convinced that it is not a man-made contract of convenience. It is a divinely appointed institution whereby we can learn to become more like our Father in Heaven. Marriage is a class that teaches us things we literally cannot and will not learn in any other way.