Part of what it means to be human is to be like God. From the first mention of man in the Bible, before we are formed God has chosen to make us in the image of God, in the likeness of God. This is not an isolated passage, either; the theme continues throughout the whole of the Bible.
The Law of Moses calls the people to be holy because the LORD God is holy. It calls people to observe a day of peace and rest because God observed a day of peace and rest. God's actions establish a pattern for our actions; we acknowledge that imitation even in our calendars, which still recognize a seven-day week and a weekend.
Jesus calls us to be perfect because our Father in heaven is perfect, and to love both our friends and our enemies because God's love extends to all mankind, the just and the unjust, even to the evil. He tells a parable where the master's forgiveness should lead the servant to forgive as well. He even speaks of being born again of God's spirit, and becoming children of God. And Christ tells us that as he has loved us, so we are to love each other.*
John's letter also speaks of us being the children of God, and again that our character flows from God within us: God loves us first, and so we love each other.
In Paul's letters, he also echoes Christ on loving each other as God loves us, forgiving each other as God forgave us. He calls us to be imitators of God. It is not too bold or presumptuous to imitate God; in fact, it is part of what it means to be human. Regaining that image of God is a core part of our redemption.
The question, if we want to be like God, is then: What is God like?
* This goes beyond how we usually understand "What Would Jesus Do?" slogans. Those slogans picture us going about our daily lives and when a moral question comes up or when a temptation arises, then it calls us to ask ourselves "What would Jesus do?" But this kind of "bailout morality" would not call us to transform our work week into 7 days, or try to establish justice throughout the land. This "image of God" way of being like God does more than scratch the surface or guide us when we are unsure. It gives us a new direction for certainty, a new goal for transforming the structure of our lives, a new set of possibilities for how to pursue the good.