From at least the fourth century it has been the custom of the Western Church to read the Passion narratives in Holy Week, obviously because they relate the events which are being celebrated. They were traditionally sung by three deacons who sang the parts of the Christ, the other voices and the narrator respectively and after the Protestant Reformation the tradition was continued with the addition of chorales at various points during them.
Before the revision of our Mass after the Second Vatican Council the Passion according to Saint Matthew was sung or read on Palm Sunday, that of Mark on Holy Monday and that of Luke on Holy Tuesday with the Gospel of John being read on Good Friday.
With the revision of the Mass and the development of the three year cycle of Sunday Mass readings, the Passion according to Matthew is read in the Year A, that of Mark in Year B and that of Luke in Year C, while that of John is still said or sung on Good Friday every year.
Apart from this being the tradition of the Western Church it is obviously appropriate to hear the Passion according to John on the first day of the Paschal Triduum during which we celebrate the sufferings, death and resurrection of the Lord. That it should be the Gospel of John which is read on Good Friday because it is in John’s Gospel that the Passover mystery of Jesus’ death and resurrection is most clearly presented.