Did John write the gospel of John?

Last Saturday at evening Mass one of the priests in his homily stated that John, the beloved disciple of Christ, did not in fact write the gospel of John. What?! I had never heard of this before so naturally, not only was I annoyed, but my interest was piqued. Why do people that are suppose to be knowledgeable make emphatic statements that are at the very most suppositions or perhaps "best guesses" of "modern experts" that they have heard or read about? It's irritating, annoying, and at the very least spreads confusion among the common people.
So, I went hunting for what the Catholic Church, in all her wisdom, teaches about this and found, not to my surprise, that John wrote the gospel of John. Here is an excerpt from Mark P. Shea, Catholic writer found on www.catholic.com:
The facts are these: The Tradition of the Church, supported by the unbroken line of patristic testimony, as well as internal evidence from the text itself, is that the Gospel is rooted in the testimony of the apostle John, son of Zebedee. Numerous other witnesses in the second and third centuries corroborate St. Irenaeus’s testimony. In addition, various elements within the Gospel strongly suggest John as the author. Most obviously, there is the attestation of the witnesses penning the Gospel that it is the testimony of "the disciple whom Jesus loved" (John 21:20)—a disciple to whom no one but John corresponds. The source of the Gospel is, quite clearly, a Jew familiar with the conditions of Palestinian Judaism at the time of Christ. He speaks Aramaic and Greek. He knows Jerusalem as it looked before Rome reduced it to rubble in A.D. 70. And he gives countless details which, if they are not the testimony of a first-hand eyewitness who was present at the Last Supper, are a singular occurrence of novelistic realism 19 centuries ahead of its time. That he was part of Christ’s "inner circle" of Peter, James, and John (cf. Gal. 2:9) is even more likely given that he was the disciple at the Last Supper who laid his head on Christ’s breast. He can’t be Peter, who is distinguished from him in the text, and he can’t be James (who died in the early 40s). So it all points to John. Additionally, the patristic tradition that the Gospel was composed in Ephesus also points to John. First, this is the city associated with the Assumption of the Virgin who was commended into his care. Second, the Gospel repeatedly answers a sect devoted to John the Baptist with the reply that John "was not the light" but had only come to "bear witness to the light" (John 1:8). We know from Acts 18:24 and 19:1-7 that there was such a sect centered in Ephesus. Finally, the sophistication of the Gospel fits the fact that the New Testament epistle with the most sophisticated exposition of theology is Ephesians.

So all the evidence points to the accuracy of the Church’s tradition that John published his Gospel in Ephesus in the second half of the first century.

There is more-- but, you'll have to go to the weblink to read it, and it is worth reading: http://www.catholic.com/magazine/articles/did-john-write-his-gospel
Another issue, just as problematic, is should I talk to this priest about teaching controversial and erroneous things from the pulpit? or should I just forget about it? I don't know.