This is very odd indeed. The evidence on allergies has never really been promoted as strong argument against formula feeding, though it may well be in a list of 'benefits of breastfeeding' because a lot of the evidence points that way.
Obesity? Well, it's always going to be difficult to isolate the infant feeding effect from other factors, but there is plenty of evidence that breastfeeding does have a role to play, and studies differ only in how large a role. There are no studies that suggest breastfeeding increases obesity, and plenty of physiological reasons to explain why that is the case.
The other, rarer, conditions he lists are not really major public health concerns because they affect very few people, though of course childhood cancers are devastating for the individuals involved. Type 1 diabetes evidence is well-established, though, so I'd have to look again at that and see what his objections are.
The one aspect on which he does say the evidence is sound is in gastro-enteritis and other infections (antibodies, as you say, Hecate). Why would we not want support, and a public health push, to reduce uncomfortable, distressing and avoidable incidences of these?
I hope he publishes somewhere, rather than just announcing his views to the press.