Should a preacher, et al, have a right to say that the Bible is fallible?
In my entire life, I have never heard one.
Which of the two is more fallible--Bible or Science?
Of course theologians have the "right" to question the fallibility of the Bible. Many do. That is a ridiculous notion.
the bible is called perfect and nobody will ever have the right to question it.
Now you are getting into the territory of Bibliolatry and turning the books of the Bible into objects of worship.
Protestants certainly questioned the Bible when they removed seven books from it! Martin Luther famously commented that he "found no trace of the Holy Spirit" in the Apocalypse of John (Revelations). He also questioned whether either the Epistle of James or the Epistle of Jude were worthy of the Biblical canon.
The early Church Fathers included some books such as the Martyrdom of Polycarp and 1 Clement in the New Testament Canon and did not include The Apocalypse of John for some time. It was not until the 4th Century that the modern canon was adopted, but even then some of the Eastern churches still clung to the older styles.
Then we have issues of translation. For example, when the King James Bible was commissioned there was no real scholarship in modern Aramaic and Syriac (two of the languages in which texts have been preserved). So there were numerous errors.
In other words, the Bible is viewed by some as completely free of error, but certainly not all Christians see it as such.