I am fine with the basics (e.g. classical vs rock/punk vs pop based on instruments) but there’s loads of other terms that aren’t very intuitive.
What is the difference between “alternate” rock and I guess “regular” rock? What is the difference between rock and punk? What is post-(insert subgenre here, like punk)? What is pop rock (the music subgenre, not the fizzy candy rocks), and how is it different from rock pop? What makes music “progressive”? What on earth are the “blues”? What is the difference between rock, metal, hard metal, heavy metal, etc. aside from an increasing level of angriness and decreasing level of clarity? etc etc
It sounds like you want a clear set of rules as to what defines every possible genre of music, which does not and cannot exist.
Genres only exist for the purpose of subjective comparison. Anyone can create them by taking some elements common to several pieces of music and labelling that as a genre. There’s no master list or governing body that decides exactly what constitutes ‘art rock’. It just is.
Use them as labels if you find it useful to make a distinction that they allow for. If you don’t see the difference between death metal and heavy metal, great - you don’t need to.