It not really about them being essay based. What matters is that these subjects (particularly Economics and History) have a lot of content, which is difficult to remember and apply throughout your essays. Nevertheless, you can do it.
Don't let teachers tell you that you aren't capable of doing a subject, many people are told that in school by their teachers and turn out to get a 1st in their degree. If you think you are able to study it then go for it. You would know yourself better than a teacher.
If your teacher is under supportive I would urge you to study the subject they teach elsewhere if it means a lot to you. Nothing worse than a teacher who oppresses you. I actually think that this can be really damaging for a lot of people.
If you're happy with your choices then hand the form in also look at other places to do your A levels if means avoiding an unsupportive teacher in a subject that really matters to you.