Public support is a factor. No one tells the wrongly accused that they are heroes and thanks them for their enduring fight against injustice. Obversely, I know people who wear their military uniforms off duty when they're feeling under-appreciated and want a little recognition, most of whom have never been involved in combat. I've known guys who came home from Camp Buehring who described their biggest problem having to choose between steak and lobster each night. Do you think they correct anyone who thanks them for their service?
Control is another. Becoming known as a pedo because the police wrongly arrested you on suspicion of it is pretty out of one's hands. You don't just say, "Sorry, you have the wrong person, I'll be leaving now" and walk out, and you'd be lucky if the news spends the weeks following report of your exculpation saying anything similar to "where there's smoke there's not necessarily fire". And you could be locked up through your trial and beyond if the system fails and your family turn their backs on you. No one knows for certain how long something like that can last.
If you were in that circumstance, you'd have to weigh the very real possibility of never getting to watch your child grow up or play a part in their life, of having them suffer outside of their control because of you, and the possibility that they will grow up to have doubts about you because of how others responded. You might never get to know your child, and they might never get to know you, and they might decide they don't want to.
And troubled teens need someone they can trust and rely on, not someone they think is only trying to help them because they're secretly trying to take advantage. Think of all the people this guy might have helped or interacted with who suddenly got accused of being molested or having sex for help by other kids. Hurting the people you want to help is pretty close to a worst nightmare for someone in that position. Coming up with these points was a pretty basic exercise in empathy.