100% with LW not being the brother's doctor, and the LW having no idea what's good for the brother. So many "healthy" foods aren't healthy for a given individual, and that's even just reducing "healthy eating" to the nutritional effect on physiology.

But also, it's not still lW's call if the brother is perpetuating their ill health. I mean, the LW's fear about losing their brother is totally reasonable, and there's probably a way that the LW can approach the brother to say "hey, bro, I love you, and I know the cancer is your trauma and not mine, but would you be willing to help me negotiate my fears over your health?"

Obviously there's a spectrum on intervention. I'd be more comfortable with the LW trying to intervene if the brother was avoiding chemotherapy because he'd read a website about copper bracelets and bleach drinking, etc. But ultimately, it's the brother's body, and since this isn't a public health issue (unlike anti-vax), and there's no indication that the brother has reduced faculties, the LW has to let the brother drive.

I wish after the columnist had said

I consulted Avi Shmueli, a psychoanalyst, about your problem. We agreed that at the heart of your letter was, understandably, fear of losing the family you have left.

that the next part of the letter had been "and so here are some ways you can work with with your grief and anxiety."