Why did Jesus wait to be baptized?

Was discussing infant baptism earlier and was laying out my reasons for thinking infant baptism is acceptable and maybe even a good thing. The person I was talking to asked if we are supposed to be baptizing infants why did Jesus wait until He was an adult. My answer was that Jesus was born under the old covenant and thus circised. When He started His ministry He initiated it with His baptism which is the symbol of the new covenant. Do you agree? Why do you think He waited until He was an adult?