My parents had no role in picking my subjects - they pretty much said choose what you want. Even though my parents werent the type to interfere, I made it very clear from the outset of year 11 that I was in charge of everything related to my education. I gave them my "Australian Government" speech. I told them that the HSC would work like Australia, they were the Governor General - the Heads of State who held no power and I was the Prime Minister who held all the power. It was probably redundant, but I wanted to make it absolutely clear that they werent to interfere.
Ironically, when I went to drop Chemistry, the school called my parents in for a meeting, because the school were hoping they would talk me out of it. My parents told them that they had no control over what I did and it was my call.
A long story, but at the end of the day, you are the one sitting the HSC and outside interference from others does nothing to help (it makes things worse usually).