Everyone uses the Feeling function, just like the other 3 functions. We probably use all 8. The difference is how much we use them and in what order.
No one said that Jungian Cognitive Functions explain 100% of human cognition or even close to it. However it becomes clearly apparent when you know what to look for that we do operate according to these functional stacks.
I tend to get confused about how similar Feeling in a Jungian sense is to things like emotion, and likewise how similar Thinking is to thoughts. Still, whatever is measured by JCF, it is real - or at least, an effective way of interpreting people and information.
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Our minds flow but the models, inherently static, used to capture its processes remain appropriate approximations. It is a basic framework for interpretation, and as such works better in theory than in reality, however is becoming more and more viable of being applied directly to human matters. Our cognition can be interpreted along any number of other such models, and so just because one is good, does not mean an unrelated approach will not also be good. The mind is a multi-dimensional entity, and we see different patterns when we change our criteria of perceiving, just as a kaleidoscope. So the patterns of JCF, as prominent as they are, could very well be left out of a rather comprehensive analysis of the human mind. And, to be comprehensive, one cannot stop at JCF, but must examine the cognition which exists outside of this framework, of which there is much.