Belichick traded All Pro OG Logan Mankins after one Mankins complained in one interview.
I actually remember when all of that went down, that whole issue was Robert Krafts ego
Mankins was pissed because the year he was supposed to be unrestricted free agent was the season in which there was no CBA (that controversial "uncapped year") so they tried to get him on some cheap restricted tag.
Mankins got low balled on the contract offer so he called out Robert Kraft as an owner, questioned his integrity, questioned his desire to build a complete team, and then demanded a trade. Kraft got pissed and rumor has it the status of the contract negotiations was going to be based on Mankins making a public apology. Mankins apologized to Kraft personally but when they asked him to make a public apology Mankins supposedly left the room and refused. Kraft insulted him with a low contract offer and then insulted him by demanding "hey go humiliate yourself to the media on my behalf so I'll look strong to all the other owners and save face for my own ego"
Mankins sat out the first 7 games and then basically said "if you franchise tag me next season your dead to me".
Kraft caved and paid him but to try to get back at him did the whole "you gotta take a pay cut" routine a couple seasons later and that led to his trade. Kraft was basically trying to personally get back at him because he made him look bad as an owner and him and his agent won the whole "whose gonna cave first" thing during the 2 years of negotiations.