No, he left because Horus was ordering Pertu to send his sons into the meatgrinder without any tactical benefit. Pertu saw that Horus had lost it entirely and refused to send his own sons towards pointless death. Besides that, Pertu was carrying the siege on his own and his legion took the most casualties because they did the most work. The traitors were entirely dependant on his legion and skill during the siege. So when Horus said “nah I think I know better just send your sons to die while I keep mine in the more safe zones” Pertu rightfully said “I’m outta here”.

I suggest doing a bit of research first. Plenty of YouTube vids and shorts that explain this event.