Query

Right is something you are entitled to, may be legally or otherwise and obligation is like a liability for you in return for your rights.

For Exp -  You have right to speak and to express your ideas with complete freedom, but at the same time you have an obligation of not to use vulgar/unparliamentary language or to hurt sentiments of others through your words.

In legal world, lets say you entered into a contract to buy a house for Rs. 10 lakh.  Now you have right to get the house and obligation to pay the money.

For a same person both the terms are vice-versa.