I'm a GP. My surgery operate a triage system - if you ring up or walk in asking for an appointment, then you get put on the triage list, and get a phone call from the doctor that same day, who can then make an appointment for you if you need one.
When patients ring up or walk in, the receptionists who speak to them will ask for a brief outline of the problem. This means that, as we usually have at least 3 doctors doing triage at any one time, we can prioritise the calls - if if see things that I know will need an appointment, then I will call those patients first so that I can get them into the surgery on the same day, often within the hour.
If you refuse to tell the receptionist what the problem is, and there is therefore nothing next to your name on the triage list, then I leave you until last. I'm not going to prioritise you over people I know will have to be seen, when I have no idea whether or not you will need an appointment. Therefore, if you don't tell the receptionist, your chances of a same-day appointment decrease substantially, and you will also have last choice of appointments over the next few days - the most convenient times after working hours will be long gone.
In addition, I, like most of my colleagues, have a special interest in a certain field. As I glance through the triage list, I generally pick out patients whose problem relates to my particular field of expertise, as do my colleagues. By refusing to give even the briefest of outlines, you rule out the chance that the GP with the most relevant experience will contact you directly.
Receptionists don't have medical training. Of course not. But that doesn't make them incapable of typing a one line summary of your problem dictated by you, in order to help the doctors do their job.
And please also remember - they speak to hundreds of patients daily. Your problem will occupy their mind for a few seconds, and then they will move on to the next patient and you will be swiftly forgotten.