Marriage in India is not about finding someone to spend the rest of your life with. It is simply a social obligation. Something you do because it is expected of you. And all the instruments of society that go into making it happen are working out of that same sense of obligation.
The reason arranged marriages are the most popular flavour of this ice cream is because people don't want to rob each other of this obligation. Our obligations, the roles we fulfill, make us who we are in this system. The man therefore, is a provider and he takes up the role of providing for his wife. The wife is a child-bearer, the mother is a caregiver, the father is the one who gives the daughter away to another man and so on and so forth.
We play the game, each trapped in their own set of constraints. The other day, a friend of my father asked him why I am not married. Upon being told that I did not want to marry, he said that I should because it would make me happy and it would make my father happy. A few minutes later, without skipping a beat, he started talking about how his son and daughter-in-law don't visit him anymore.
The shift wasn't apparent to him. He wasn't happy. But he was telling my father that me getting married will make him happy. He was saying something he believed to be true. But the reason he believed so was not because his life was evidence of it. He believed so simply because it was something he had heard so many times.
We all hear it. We all believe it. We all, on some level, resign to the roles this system assigns us. Some do realise that it is not the only path to happiness, but the mythology surrounding marriage is so well-established that despite considerable evidence to the contrary, we keep believing the myth.
Perhaps the reason your parents think they are failing as parents is because they are under the impression that marrying you off is their job.
Perhaps, instead of telling them that you are not ready, you need to tell them it's not their job to find you someone to marry.
Perhaps, instead of making it about marriage and its good and bad sides, you need to tell them that when you choose someone, you will let them know.
In short, the way out of this is to free your family from the responsibility they think they have towards your marital status.