Do you have to tell your English teacher if you want to drop a subject?
I thought usually you talk in person or email (more likely) the deputy principal or your stage head teacher to request to drop a subject.
But either way, i think you shouldn't bear too much thought on what you teacher thinks even if you do end up telling them that's the reason why you want to drop. It's not like they are the one sitting the assessments and eventually HSC, right? I think before you said your school wasn't really supportive regarding wellbeing, but remember, what you are experiencing may not be perfectly understood by the teacher and you should do what you believe is good for you in the long term. (I hope that makes sense)