To head off something is to stop it before it can happen. Getting in front of it and turning it aside.
The image is from herding, where you head off an animal by getting ahead of it. It splits round an object, and heading off a crisis, a question or a rebellion all mean preventing them in advance. There is a completely separate and very common sense meaning to leave, since heading off home is what people say when a party is winding down.
Practised in Phrasal Verbs, A Man Called Ove
First appears in chapter 6 of A Man Called Ove.
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