Congratulations — you obviously paid attention in your primary school English lessons. I, too, learnt about the parts of speech and the definition of "pronoun" when parsing a sentence, at about that age.
I have also been lucky enough to have the privilege of being able to continue English lessons into secondary school, and at these more advanced levels you learn of a difficult concept called "context". It means that a word can actually mean different things depending on when and how you use them!
For example, "hands" are those wiggly things on the end of your arms, but in the context of the phrase "all hands on deck", the word actually means whole people! (This particular type of figure of speech, where a part is used to represent the whole, or vice versa, is known as synecdoche.)
Someone might say "I don't use drugs" and, in nearly all circumstances, through a careful consideration of the context, most people would take that to mean "I don't use illegal recreational drugs", rather than retorting with "Aha, but I saw you take paracetamol with a hot caffeinated drink yesterday, and I know you're on sertraline!"
Similarly, someone might say "I don't have/use/do pronouns" to express disagreement with others requiring them to state their pronouns or to use particular pronouns for others, and only the very obtuse or facetious would ignore the contextual clues and say, "Aha, but you started that very sentence with a pronoun!"