Are you sure you're not confusing cause and effect? Like maybe your view of "intelligence" is limited to the definition used by IQ tests. That would be kind of unfortunate because it selects for a certain type of test taking ability, mostly related to logic puzzles and spatial manipulation and vocabulary. Those skills might be useful in academic and some professional contexts, but they don't really benchmark the entirety of human potential.
Human intellect has the capacity for creativity, empathy, wisdom, self awareness, diplomacy, etc., and those aren't as easily measured on an IQ quiz.
Just my 2c as someone who's not professionally trained to apply IQ tests but have studied them as a side interest, and scored highly on them (probably like many others here). It's just one biased facet of our minds, and we shouldn't give it undue weight or rule people out because their minds work differently.