Seems a sharp kid, can see why Pep like him so much - at the start anyway. Anyone with any credible info on what ultimately happened to him under Guardiola?
Back when Højbjerg moved to Augsburg on loan, he was interviewed by Danish media. He basically told that he had - perhaps too early on his career - big ambitions (most likely about playing more), and that Pep wanted to take it slow with him. He also confirmed that regrettable things were said between the two because of this, and that it caused a rift between them. He stressed that he has all the respect in the world for Pep, and that he's a fantastic coach... on the field. Basically he's mirroring what Zlatan stated back then but in less controversial terms.
Lastly her stressed that it isn't his job to be best of friends with his coach, but to do what he's told.
So yeah, all in all it was most likely a clash of personalities, but never a matter of professionalism.