Professor Bainbridge explains the problem with public sector unions. He gives a good analysis, which I recommend in its entirety, but here's what I take to be the key paragraph:
A core problem with public sector unionism is that it creates a uniquely powerful interest group. In theory, bureaucrats are supposed to work for and be accountable to the elected representatives of the people. But suppose those bureaucrats organize into large, well-funded, powerful unions that can tip election results. With very few and very unique exceptions, no workplace in which the employees elect the supervisors functions well for long. Yet, research by Terry Moe (22 J.L. Econ. & Org. 1) into the electoral power of teachers' unions finds just such an outcome.