“Matthew is authoritative because the Words of Christ are recorded in the Gospel.”
No. If that were the case, then this thread could become authoritative by simply posting verses from the Bible. That would make every book ever written by every heretic authoritative if he merely uses Bible verses in some fashion - whether or not they are used properly!
You approach from a false premise.
Are the NT scriptures authoritative because church officials placed them in the canon; or were the NT Scriptures placed in the canon because they were authoritative?
While Catholic doctrine IS 'authoritative' because the MAGISTERIUM says it's so.