As a neutral outsider, Zlatan's claims make no sense. Why would any successful manager, out-of-the-blue decide one day to bench a star player with no explanation whatsoever?
Some of Zlatan's claims do ring true - Pep's avoidance about talking to him after this fallout seems true.
What I think transpired is that Pep was forced to choose between building a team around Zlatan or around Messi. Once having chosen Messi, Pep likely instructed Zlatan how to play to fit in to his expectations - i.e., by taking up a supporting role. Zlatan's ego is such that he'd ignore such advice. Eventually, Pep decided that Zlatan wasn't playing in a manner that helped the team get the best out of Messi's abilities - and Zlatan got less and less playing time.
Equally, Pep avoided talking to Zlatan about this situation, not wanting to get into a heated, emotional confrontation. Pep's solution - trade Zlatan.
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I haven't read Zlatan's book - but I've read portions or synopses of portions about the book on the Internet.
Some of Zlatan's quotes around this incident are supposedly along the lines of:
"Pep is not a man. If he were a man he wouldn't be afraid to talk to me."
"Pep is a coward. I wanted to talk to him man-to-man and settle it."
"I'm 6'-5". If that coward Pep would have talked to me, I'd have settled things man-to-man."
Etc.
I'm paraphrasing... but it's clear that any discussion of this topic with Zlatan would have been heated and may well have resulted in physical confrontation. Pep simply didn't want to endure such a confrontation.
