Laine's departure from Wings -- and in fact the dissolution of Wings overall -- seemed a bit murky for 40-some years.
Supposedly it was a "mutual decision" for him to leave, and there were a variety of semi plausible explanations, but all parties remained "grimly stiff-lipped" over the whole deal which led you to believe it hadn't really been "amicable."
What supposedly happened was, in January 1980, during the course of a Wings tour following the moderately successful LP Back to the Egg, McCartney was busted in Tokyo carrying half a pound of pot, jailed for 11 days, and released. The remainder of the planned world tour was canceled and future tour plans thrown into question.
Supposedly Laine and McCartney, who from all external appearances seemed to get along all right, were butting heads over-- surprise -- songwriting credits. McCartney and Laine shared songwriting credits -- you would think 50-50 -- for "Mull of Kintyre," which in 1977 had become a mashive UK and international hit (although not so much in the US).
But instead of a 50-50 split of the songwriting royalties, Laine was paid a flat fee, a pittance compared to what full cowriting credit would have been. So Laine was feeling exploited and undervalued, while McCartney undoubtedly harkened back to the days of the Beatles when ALL his songwriting royalties were split, so he had no interest in getting back into that situation.
Laine and McCartney both remained mostly mum over the years over the whole deal, neither trashing each other or speaking with any fondness over their years in Wings, which seemed a little weird because Wings was hugely successful in their time and Laine had been a significant part of it.
After 30 some years of somewhat chilly mutual indifference, both parties seemed to thaw out a bit in the 2010s -- McCartney rereleased most of his Wings material and spoke positively of Laine's involvement and Laine told some funny stories about his tenure with the band.
There were also some hints that some of the differences might have involved friction between Linda McCartney and Laine's wife in the Eighties; by the 2010s Linda had pashed on and Laine gotten divorced so maybe those problems had dissipated.
Upon Laine's death this week, McCarthy posted cordial but not effusive memorial messages.