Nobody is saying he shouldn't take time out if he needs it, what people are saying is that a) his mental health should be taken into account when scheduling his shows and appearances because, unlike a freak leg break accident, someone with diagnosed mental health and medical issues knows about them beforehand and therefore should be taking them into consideration during the planning stages of the tour, not just cancelling mid-tour and b) if he does need to take time out there is a way to announce it without alienating people who have paid for tickets by essentially saying "Sorry I can't make the gigs that my fans have paid to see me at, I want to focus on Glastonbury where I'm not even headlining"
Both of those things should be handled properly by his management.
The tour schedule should have been made taking his medical info into account - just looking at the tour schedule as a lay person it is a lot, of both performing and travelling. As someone with anxiety there is no way I could manage all the stress and pressure of that schedule, so why was nobody in his management team highlighting this and trying to work in places where he can have a break or ease the pressure?
It is far easier to set a schedule where you do fewer gigs but leave room for either rest breaks or adding in extra dates (even if they are small "secret gigs" done in more intimate venues) than schedule that you are more than likely going to cancel half of. Or even just streamlining the tour schedule to minimise the stress of the travelling etc.
I remember in my student days there would often be big bands doing "secret gigs" during their tours - ie smaller venues where tickets went on sale a few days/hours before the gig - when they were on tour, so my friends and I would always look for where there were a few days break in a tour schedule, especially if they were coming to one of the cities nearby, and keep an eye out for secret gig tickets on one of those dates. We got to see so many great bands that way for much less than a full gig ticket would have cost. It didn't cost a lot to put those shows on as it was often just a pared down show - the band, instruments, a stage and a hall, no fancy lighting or pyrotechnics etc - and the venues got more in the way of publicity than payment (especially if they started getting a rep for always getting secret gigs when big stars were in town)
As for the actual announcement, there are much better ways to word a cancellation announcement that don't make it sound like he just wants to prioritise one event over another because of its prestige - everyone wants to perform at Glastonbury but that doesn't mean you have to tell everyone that you're going to sacrifice them to make that happen.
Again, management should be stepping in to advise him on what not to say - he doesn't have to talk about his mental health or go into any great detail but it was specifically highlighting Glastonbury that was the issue for many, so all he needed to do was say "I need to take a break, so I'm cancelling everything until at least the end of the month to give me some time to recover. The tour and the schedule is just too much for me and I feel like I'm not at my best. I don't want to do that to my fans so I'd rather disappoint people by cancelling and rescheduling for when I'm feeling better than disappoint people because of the sub par performance they would get otherwise".
Then he could have either added something like "I'm hoping to make it to Glastonbury at the end of the month but I'll update you with a decision once I've had some time away to focus on recovering," or just left Glastonbury off the post altogether and made a separate one a few days/weeks later to announce that he was feeling better after taking time out and was aiming to have Glastonbury as his return performance.