Hi Drearyweather,
Church required a verse that says it is appointed by God, hence they added such portion in Mathew 16:18. Context of this verse is Jesus’ famous question “Who do you say I am?” However, if you compare this portion with its parallel account in Mark 8:27-38, you will find that Jesus never made such church-friendly sentence. Jesus had unequivocally declared that he won’t appoint any church or organisation to work on his behalf after leaves the stage till the end of the world (Mathew 7:21-23), and judgement is based on whether a person acted humanely or not, not according to one’s religious affiliation or worship (Mathew 25:31-46)
Such additions being made to what Jesus originally said was common in early days. Hence Luke deleted whatever added in his life-time. (Luke 1:1-3) For example, teaching about ransom sacrifice of Jesus was a Church doctrine which they added to Mathew 20:24-28 which is not found in the parallel account of Luke 22:25-30