Little history lesson, bear with me;
There was once a man called Thomas Wentworth who was a member of parliament in England. He supported "The Petition of Right", a bill that was intended to restrain the power of the king, which was Charles I at the time. He was later offered a position on the King's privy council and became deputy of Ireland. He then began supporting moves by Charles and his supporters to gain more power for the crown.
See, when you're in a position that has certain inherent interests, you often end up supporting said interests. If you end up in a different position, sometimes your interests will change. As a player you want to accomplish things with your own character, but as a GM you want the entire RP to succeed. Just like Wentworth, changing roles can often mean you end up supporting a different set of values than you previously did.
And I don't mean to accuse anyone of being selfish, no; its just a matter of fact that certain roles come with certain implied interests. They don't even have to be purely selfish interests; maybe the GM wants to treat everyone fairly, while the player thinks if they get things their way the RP will be better for it. The only thing is they can disagree on what should be done due to being in different positions, and when those positions change their interests can change too.
Just my two cents. Tl;dr there's a GM you and a player you because the two roles come with different interests.