The phrase "to fulfill all righteousness" is a term of art. It is used to mean "Keep the rightous demands of the law".
In this case it is a demand by Jesus to John that John reconsider his refusal to baptise Jesus. John properly refused to give Jesus the Baptism of Repentance. Since Jesus had nothing to repent of, it would not have been right to recieve this sign.
Jesus then demanded to be "to fulfill all righteousness", or for the purpose of keeping the Law. Since the Law required many different baptisms in addition to the Baptism of Repentance, he was asking for a different one.