The reason I personally want to try for medicine is because I excel at Sciences(never been pushed in that direction by my parents) and, even though it sounds cheesy I think being a doctor is one of the most worthwhile jobs you can do which includes science, specifically chemistry/biology.
However, at my college, there are a few asians (Indian, Pakistani, Bangledeshi etc) that want to do medicine but really haven't thought it through, they don't have the minimum requirements in terms of grades but still choose that path is for them. I suspect these people are going in that general direction because of pressure at home.
The reason asian parents push their children into careers like law/medicine is because (as Oliver stated) they're high, prestigous postions in society. Generally speaking when first generation asians arrived in the UK they were treated like crap initially, had no chance of a proper education and had to work from the bottom up. They don't want the same for their children so they push them to do better and take the oppurtunities that they didn't get.