The Indian caste system is misunderstood in the West.
That you have to do what your caste prescribes (as far as profession goes) has not been true for a long time. In fact, most Indian castes are medieval professions by nature. There's no caste for "doctor", or "engineer", or "call center receptionist".
If you are going to make comparisions between the Indian caste system, and Western society, then compare it to fuedal Europe. If you were a cobbler's son in 15th century England, what would you do when you grew up? Chances are, you would become a cobbler like your father, his father before, him, etc. In fact, the origin of many Western last names (like Miller, Thatcher, etc.) come from professions. In that respect, there was very much a "caste system" in Western society, or for that matter any other society you look at. Social mobility is an extremely new concept. It was just more rigidly defined as such in India.
In an effort to address alleged wrongs about the caste system, the Indian government instituted a system of affirmitive action in the 1950's. Whereas affirmitive action in the West has never been about quotas, in India, it has always been about quotas. If you're a lower caste Hindu, you have X number of seats in the university, and public sector jobs reserved for you. You can also compete for the general (non-allotted) quota. If you're an upper caste Hindu in India today, there is basically nothing left for you. I have several relatives in India who are doctors who are sitting at home doing nothing, because the government refuses to let them work because the quota for upper caste Hindus has already been filled. Meanwhile, the doctor-to-patient ratio is like 1/100th of what it is here.