The Church of the Brethren actually have six ordinances which include the love feast, the anointing with oil, the laying on of hands, the assembling together for worship, the holy kiss, and trine baptism.
There are several reasons the Church of the Brethren believe in trine baptism which means to baptize the person face forward three times. One reason for the face forward aspect of baptism is that baptism pictures our crucifixion with Christ and John 19:30 says that when Jesus died on the cross “he bowed his head and gave up the ghost.” Therefore baptism face forward is a literal application of the Scripture. The identification with the death of Christ pictured in water baptism by immersion is the death, burial, and resurrection of Christ (Romans 6:1-4) not all of the details of the death of Christ. Because Christ was nailed to a cross, does this mean that this detail must be duplicated in baptism.
The three times forward aspect of water baptism is based on the Trinity in the Great Commission in Matt. 28:19-20. Each baptismal candidate is baptized forward as each name to the Trinity is mentioned. In the Great Commission of Matt. 28:19-20, Jesus said to baptize “in the name (singular) of God the Father, Son, and Holy Spirit.” Baptizing once in the singular name of the Trinity emphasizes the deity or essence of the Trinity. There is no evidence from any baptismal passage that the converts were immersed three times face forward. Also in Acts 19:5, the believers were baptized in the short formula of Jesus’ name only and therefore were not baptized three times.
The Didache, also called the The Teaching of the Twelve Apostles, and written around the turn of the 1st century is referenced as evidence for trine baptism. The part quoted reads: “But concerning baptism, thus baptize, ye having first recited all these precepts, baptize in the name of the Father, Son, and of the Holy Spirit, in running water.” “The Didache states that if immersion is not possible then water was to be poured three times on the head (chap. 7). Notice that this early work does not say to immerse three times, only pour three times” (Ryrie, page 491).
Ryrie also states that “Proponents of trine immersion point out that some lexicons say that baptizo means to dip repeatedly but some do not). The evidence for this view is not strong” (page 492).