if you want to become doctor u have to study mbbs, for lawyer u have to study law,for engineer study BE etc?

BECAUSE POLITICIAN REQUIRES NO SUCH EDUCATION.HE SHOULD BE A GOOD MANIPULATOR AND MUST KNOW PRIXLES OFTHE EVER MOVING TIMES .
"A politician or political leader (from Greek "polis") is an individual who is involved in influencing public decision making. This includes people who hold decision-making positions in government, and people who seek those positions, whether by means of election, coup d'état, appointment, electoral fraud, conquest, right of inheritance (see also: divine right) or other means. Politics are not limited to governance through public office. Political offices may also be held in corporations, and other entities that are governed by self-defined political processes."

Many politicians went to law school because so much government is shaped by the law.

your idea is good. i think this was debated long ago. people also deliberated adult franchise (eligibility for voters also!). Finally, considering our literacy rate, our agriculture background (where most of them don't have much formal education), educational qualifications have not been made mandatory.

Political science really wouldnt prepare someone to be an effective legislator. You really have to understand the law in order to be effective at making them. A law degree would be the best for most politicians.