To understand why some think the writer of the Revelation could not be the apostle John, a bit of historical background to things that happened in and after the second century A.D. will be helpful. This is taken from an Introduction to the Bible book of Revelation in the Study Bible cited:
"Many Jewish apocalypses were written after the close of the OT canon,
at a time when Jews believed that prophecy had ceased and that the
word of the Lord for them was primarily to be found in the Law and the
Prophets. These Jewish writers therefore wrote under the names of
earlier godly persons such as Ezra, Baruch, Enoch, Isaiah and even
Adam so that their writings would gain credibility and acceptance.
These works are called pseudepigrapha (literally 'false writings')
because they were written under pseudonyms. Similarly, in the
post-apostolic era, fanciful writers and false teachers returned to
this practice by using the names of earlier followers of Jesus (such
as Peter, James, John, and even Mary) to gain a hearing from
Christians." New Living Translation Study Bible, p. 2164, 2008
This is pertinent to the question because it shows how the earliest seeds of doubts about authorship of sacred Christian literature were sown. Whereas the belief that the apostle John was the author of those seven letters sent to seven churches in Asia was not a problem when they got their letters, once more writings appeared under the name of 'John' some might then think the Revelation could have been by this John and not the apostle. Given that the apostle likely died soon after writing the Revelation (given his advanced age) later writings by someone called John could not possibly be the apostle John, so maybe the Revelation had actually been written by this other John? Seeds of doubt slowly sprout.
By the third century such doubt began to flourish. Here is another quote in another Introduction to the book of Revelation:
"In the third century, however, an African bishop named Dionysius
compared the language, style and thought of the Apocalypse
(Revelation) with that of the other writings of John and decided that
the book could not have been written by the apostle John. He suggested
that the author was a certain John the Presbyter, whose name appears
elsewhere in ancient writings.
Although many today follow Dionysius in his view of authorship, the
external evidence seems overwhelmingly supportive of the traditional
view." New International Version Study Bible, p.1882, 1987 edition
It would therefore seem that the earliest open challenge to the authorship matter arose in the third century, due to Dionysius having read other religious literature written by John the Presbyter. What did the early Church believe about who the author was?
"In the early church, this John was generally identified as the
apostle John, who refers to himself in the Gospel bearing his name as
'the disciple Jesus loved' (John 13:23; 19:26; 20:2; 21:76); in his
epistles, he calls himself 'the elder' (3 John 1:1)." New Living
Translation Study Bible, p. 2164, 2008