What is ironic about Troy's job as a garbage truck driver in Fences?
Troy had complained to the management at the garbage company about discrimination. Troy claims that the reason he cannot get a promotion to the position of driver is the result of systematic discrimination.
He has noticed that only white men are promoted to driver, and, although he possesses no driver's license, Troy complains about the injustice of a system that favors one race while excluding another.
After Troy's complaints result in a promotion to driver, we find out that Troy does not have a driver's license. This is an ironic situation in that Troy's complaint is shown to be purely abstract and even might be said to be based in his own prejudice and entrenched biases.
He is applying a generalization to his experiences which is very similar to the same kind of race-based bias he argues is holding him back on the job.
Also, more simply, Troy is complaining about not getting a job that he is definitively unqualified for.