Your logic is interesting. I mean what CAN GPs treat? If they CAN'T treat women because they are specialists in women's health, then it follows that they can't treat anything!
Most people who present at GPs surgeries will have illnesses that won't need different treatment depending on whether they are male or female. Surely you actually see that "specialising in women's health", is not needed at GP level.
If they can diagnose tonsilitis prescribe without being an ENT specialist, or treat tummy ache and D&V without being a gastroenterologist, or treat a headache without being a neurologist, they can treat a woman without being a gynaecologist.
Hey news flash, sometimes someone maybe has flu and has stomach ache, feels sick, is running a fever, has a runny nose, sore throat, tight chest, ear ache, bad headache all at the same time, and the GP stills sorts out antibiotics for the ear and chest infection, decongestant, paracetamol to reduce to headache, fever and stomach ache... all at the same time with no specialists in any area. Like they can do all that and yet can't treat a women because they aren't a gynaecologist. RUBBISH