Those people who suggest not to get married without parents' approval,then should we give up infront of our parents,and let go of each other?
Nothing to be confused about, listen forget parents approval at least get one parent on your side before you get married to him. This way you will have more leverage when arguing your point of view in front of the parent that does not agree with you. Parents love us and want us to be happy.
From what I gather, your parents said no because of the attitude of his mother. Convince your parents this is not the case. How old are you? Is it imperative to get married right away? Like MKD said, talk about marriage to him with your mother from time to time and do not give up. Mothers are usually the ones who can understand their children better and give up quickly but in this case you can target your father. Daughters are fathers soft spots. Tell him how much you love this guy and getting married to him would mean the world to you. If he sees how happy you are I am sure he will accept it and then it will be easier to convince your mother.
At the same time while you are doing this, ask him to do the same thing at his home. I did not gather in your post whether his father is against it or not. If he is neutral then it is good opportunity for him to get his father on his side. Once his father is with the son, mother will oblige too. Get married to him, with approval and love because that is the way to go. Not saying you should not get married to him. Just wait it out a bit and have patience.
After all, it is your life and if you have been with each other for 2 years and you do love him and trust him enough to contemplate marriage with him then you should be strong enough to let your love for him be known to other people and make other people realise the fact and give their blessings.
If you will run away or elope then you have already done something which will piss both your parents and his parents off. If you run away or elope then you will have to start from negative to go to break even and then in to profit.
Elopement: Girl is in negative and has to work hard in getting relations good enough with her in laws to get to neutral or break even.
With Blessing even though it is just one side blessing or both side just one parent blessing: Break even point achieved, girl is neutral and just has to work to improve relations with one parent with the added advantage of having blessings and support of her parents.
With full blessings: Profit achieved and whatever hard work and effort that she puts in to the relationship with her in laws will go profit to profit, green to green (hopefully iA).