"Why, in your opinion, is there a tendency with some believers to despise prophesyings and prophets?"My answer ...
For two reasons.
1.) Some believers believe that the time of the prophets came to an end with the completion of the canon of the Bible.
2.) All believers are instructed by Scripture (i.e. Deuteronomy 18:21,22) to test all proposed prophecy by the truth test (i.e. Do the prophesyings come to pass).
"What was motivating those who attacked the prophets?
What were there reasons to revile and persecute and shall say all manner of evil against the prophets?"
The context of the quote of JESUS, referenced in the above questions makes it clear that JESUS is speaking of the prophets of the Old Testament. Those who persecuted the prophets in the Old Testament were never believers, but rather, always those in rebellion against God. Whether king, or false prophet, or common idolator, those who reviled, attacked, and persecuted the prophets of old were non-believers.
That makes for a distinct difference in your questions.