You are right.
I spent 30 years as a social worker and was always absolutely clear with my clients that they could go back to my senior manager if they felt that we were not able to work together; and that it worked the other way too.
I hope very much that things have not changed in that regard.
Put together your points; marshal them clearly; make the point that you want the best for this boy and to accept all the help that SSD can offer, but that, in order to do so, you need to feel compatible with the social worker. You need to meet them half way and not go in all guns blazing saying how hopeless he/she is; but just say that you recognise that help is needed and that there needs to be a supportive and mutually respectful relationship for it to work well. The department should respond in an objective professional manner.
Having said that, I do know that some people simply refuse to co-operate with their social workers in any way and that they can work their way through a fair few over the course of their lives! SSDs are used to angry emotional people who fly off the handle at the drop of a hat and demand a new social worker at regular intervals.
Your job is to tackle this in a calm way and show them that there ar sed reasons for your request.
If your approaches are rejected you can ask to initiate their complaints procedure. I hope that this will not be necessary.