I think a good way to describe this is the term "a chip off the old block". This term is used to describe a child as being just like it's parent, and I think it is rather fitting here as well. The chip is in fact part of the block, but seperate from it, after the ascension of Jesus, the chip was glued back to the block.
But also, we are all children of God, and Jesus led by example, he did not mean for us to put him on a pedastal, and go on our sinful ways thinking "oh we could never be as good as Jesus". He wanted to show us as a living example that we are all one with God, and we do not have to seperated from Him, the Father.