Any diet can be squeezed into unhealthy category, I agree with that. A vegan friend is reducing sugar intake and bread, because he feels that's unhealthy for him.
OP, I think it's sensible to follow the NHS link posted by Graphista, it's very supportive of vegetarians and vegans. Just as any parent does, keep an eye on his general health.
I'd like to move away from your son and mention that UK scientists are very concerned at the number of people in this country who are showing iron deficiency because of lack of meat. The Times, Saturday September 16 2017 – page 7 under Body + Soul.
Also, some veggie products (the simulating meat ones) may contain Seitan, which is 100% gluten and some people may need to be wary. The same goes for Quorn, though perhaps I ought to mention a lot of everydday bread is just as full of chemicals.
Graphista, I was blocked from opening your Harvard reference (unless I paid) but I did read the Kaiser Permanente one. Not impressed, KP are an American Health provider who has been fined millions twice for bad practice.
Although the various people cited may look impressive, many of them are evangelical vegans and can be selective their 'science'.
Esselstyn's 1985 research finished up with eighteen people and no control group, hardly science based. He believes in a whole plant based diet, certainly not vegetarian, forbidding,
“... all added oils and processed foods that contain oils, fsh, meat, fowl, dairy products, avocado, nuts, and excess salt. Patients were also asked to avoid sugary foods (sucrose, fructose, and drinks containing them, refned carbohydrates, fruit juices, syrups, and molasses). Subsequently, we also excluded cafeine and fructose… encouraged multivitamin and vitamin B12 supplements and fax seed meal,...'”
I'm not sure what he's got against avocados but I'd be worried for anyone who took up his diet.
dresselstyn.com/JFP_06307_Article1.pdf
There is plenty of UK based research (as shown by the Times article) but they don't always reflect the values of the reader. EPIC-Oxford studies are far more useful in this country. Unfortunately, access has to be through a US site.
www.ncbi.nlm.nih.gov/pubmed/16441942
“...studies of vegetarians have shown a moderate reduction in mortality from IHD but little difference in other major causes of death or all-cause mortality in comparison with health-conscious non-vegetarians from the same population. Studies of cancer have not shown clear differences in cancer rates between vegetarians and non-vegetarians. …
Overall, the data suggest that the health of Western vegetarians is good or similar to that of comparable non-vegetarians.”