The Gospel of Matthew has several incredibly strong arguments that link it firmly to the New Testament and show without much doubt at all that is should be definitely included in the New Testament. Firstly, it corresponds very closely with two other gospel accounts of the life of Jesus, so much so that Matthew, Mark and Luke are called the synoptic gospels, referring to the "common" story that they share and tell about Jesus and his life and ministry. This offers significant proof that it is accurate and reliable, as it account tallies with the account given in other books that are recognised as being part of the New Testament.
Secondly, it has overt and deliberate ties to the Old Testament, and it seeks throughout its pages to show that Jesus is the fulfilment of all of the Old Testament prophecies and promises. Matthew is the gospel that contains most verses from the Old Testament, and it also, in Matthew 1, seeks to establish a direct link from Abraham to the birth of Jesus, as Matthew 1:17 demonstrates:
Thus there were fourteen generations in all from Abraham to David, fourteen from David to the exile to Babylon, and fourteen from the exile to the Christ.
The genealogy that begins the gospel thus presents Jesus as a direct product and outcome of the Old Testament. Lastly, the Gospel of Matthew should be included in the New Testament because it is the gospel that was used most by the early church, and it was cited by the early church fathers more than twice as often as other gospels. This indicates very strongly that the early church immensely valued this gospel, and therefore church tradition supports its inclusion in the New Testament.
The Book of Matthew was extensively quoted by biblical scholars during the first and second centuries A.D. Matthew begins by documenting Jesus' lineage back to the house of David and then to Abraham, Isaac, and Jacob. The Book of Matthew provides a transition between patterns of thought in the Old Testament and the New Testament; therefore, it is essential that it is included in the biblical canon.
The first chapters also discuss the miraculous nature of the birth of Jesus and his interactions with John the Baptist. This account of John the Baptist as a supporting figure of Jesus must have been particularly important for early Christians, as there certainly must have been many individuals who accepted John as a messianic figure also.
The following chapters also include Jesus' Sermon on the Mount which delineates some of the most basic principles of Christianity. Furthermore these new principles enforce a "new law" and a new code for ethics in relation to Old Testament thought.
The middle portion of Matthew then documents Jesus' miracles, parables, and death. The last portion discusses the resurrection. The Book of Matthew is a documentation of the entire life of Jesus, another reason to include it in the New Testament and utilize it as an introductory text.