AIBU to think saying 'I don't give a fuck' shows strong feelings?

[CoalTit]

When someone says loudly and vehemently, or even types "I don't give a FUCK!", I always take that to mean that they're actually having some big feelings.
Is that a reasonable assumption on my part?

That depends on the context. It can literally mean ‘I don’t give a fuck’, and it can mean ‘I don’t give a fuck about whatever your issue is, but I do find your bleating fucking annoying’. If there is a big feeling, then it isn’t necessarily concerning the original topic.