Power struggles, relationship friction, moral dilemmas and temptation, losing an advantage, loss of control, ego-related conflict

A parent favoring one child over the other
The coach's nephew getting the most court time 
The office suck-up being given an important or lucrative client
A teacher doting on her "chosen few," giving those students special duties and roles 
One child getting a larger inheritance than another 
A negligent co-worker escaping consequences because he's the boss' golf buddy
Being expected to overlook certain things for a preferential client
A parent being quick to believe her children over her stepchildren 
A star athlete never being reprimanded for showing up late (unlike the rest of the team)
One university department escaping cutbacks that other departments are subject to
A coveted political position being awarded to a relative with no experience
A contract bid being won by someone close to the client

Having to bite back comments that will only start an argument
Speaking up about the issue and being labeled a troublemaker
Morale in the workplace slowly declining
Being sucked into university politics
Being unable to enjoy family functions due to drama
The character's workload increasing because a favored employee is incompetent or lazy
Dealing with a child's hurt feelings over a sense of unfairness
Competitiveness turning into a personal rivalry
The character trying to one-up a favored teammate to prove their personal worth
Friction between siblings who are treated differently