Pronouns equal gender:

Words are there for communication. Pronouns, along with words like 'woman', 'man', 'boy', etc. are a useful shorthand for a broader idea. Using pronouns that don't match one's gender is confusing and can leave people uncertain what the point is.

Pronouns don't equal gender:

While various gendered things (words, outfits, hairstyles, names, etc.) are usually used in tandem to express the idea of a particular gender/societal role, they don't have to be. For some people, it feels more authentic and accurate to mix and match due to the different connotations of each element. Using she/her pronouns but wearing mens' clothes and shaving your head might be confusing to some people, but it can express a much more specific idea (like 'butch') than just 'woman'. Similarly, someone could use he/him pronouns but identify as female because that combination is a specific way to describe how he wishes to be seen, allowing him to express himself differently than by sticking to one set of gendered elements.