St Peter was the first to recognise Jesus as Lord. He was the only desciple to be given the keys to the kingdom of heaven. 1 Chorinthians 15:5 says that the resurrected christ came to him first and not to the others. He was the first Bishop of Rome and crucified himself upside down in commemoration of Christ. Therefore, with these 5 accolades which the other desciples do not pocess, he should be leading the new testament and not a tax collector called Matthew. This makes a basphemy of Christ who gave the keys to the kingdom of heaven to St Peter and not to Matthew, Mark, Luke or John.
We don't know exactly why the four canonical Gospels were chosen and the other Gospels excluded. We certainly don't know why there were arranged in the order that they were. However, the following issues may have played major roles.
(1) Apostolic authority. Matthew and John were believed by early Christians to have been written by their namesakes, and Mark was believed to have written down the testimony of Peter. Luke is an oddball in this regard, but at least it was accepted to be a genuine work of Luke the physician. The Gospel of Peter was (and is) believed to be a forgery, not actually written by Peter.
(2) Antiquity. The four canonical Gospels are the oldest Gospels we now possess. They may or may not have been the oldest Gospels known to the early Christians, but they were certainly very ancient, having been written some time before 100 CE. The Gospel of Peter, in contrast, was probably written in the second century.
(3) Order of production. It was believed that the Gospels were written in the order given in our modern Bibles, which may explain why they were arranged that way. (See Augustine's Harmony of the Gospels 1.2, for instance.)
(4) Orthodoxy. The four canonical Gospels were interpreted as orthodox in their theology. In contrast, the Gospel of Peter was believed to support the Docetic heresy.
In my opinion, momentum was probably also a major factor. Once the four canonical Gospels were grouped together, adding or subtracting from them would have meant changing the standard, which is (IMO) harder to do than to get the standard started in the first place. But this is just my opinion, and nothing I have heard from scholars. In contrast, the four points above are well-known to scholarship.