Why do some Biblical Scholars doubt the Authorship of the Gospel of Matthew?

Some Biblical scholars doubt the authorship of John because they either are not aware of, or take sufficient notice of, the various controls put in place by the early church. They also may not realize that, if John was truly anonymous there would be a range of different authors proposed by those who would have been in a position to speculate. They may also not be aware of the lack of acceptance which would have been given to such a work had it been truly anonymous. There is also confusion by some between two John's referred to in the early second century church. These are clearly two different people

Also in the second century we have a record of a church official being dismissed for passing his otherwise orthodox work off as the work of an apostle. So, not only apostolic authority, and apostolic teaching (which this work certainly had) but plain honesty mattered to the early Christians.

The Word attached to John (and all the other gospels as well), the Greek Word kata means 'according to.' This attribution was not done lightly and meant that those who did so were sure of who wrote the Gospel, even if we do not have access today to the information they had, as being obviously much further away from the event of the writing of John.

It is possible that the relevant Bible scholars are not aware of a number of these factors, or else take little notice of there importance. Many Bible scholars also accept John as genuine