I think you are misunderstanding what the Twitter audience is trying to convey in 280 characters.
When they (even I) say he fought for his love tooth and nail, it's not against the world or the family but his lover Akshara herself. He fought for her love when AK herself gave up. It's difficult to fight with family and convince them for your love I agree but it's an impossible fight when you are fighting against your love itself. He fought against AK's selfish sacrifice. He was rude, brash, and impulsive (but only towards AK, not even AR) because he felt his love gave him that right. You only take liberties with the people you love.
His getting engaged to AR was under duress(mom's bad health and he had clarified this and his terms to AR). It was NO Janam Janam ka vaada but a deal (for a family name only, not even a real companionship). The deal can be broken when you find a cheating clause. Goenkas broke it when they found out about Harsh's lie about dates so AB is also entitled to do the same when he found out about AR's lies. He didn't do it for that reason is a different story but he was not in the wrong for doing it.
I think I understand what your problem is with the situation or what I have come to understand from your post history. You tend to think in terms of social definitives like rituals (Tilak, engagement, etc. ) and you feel these are the things that are needed to make or break a relationship, but the general audience doesn't think that (or at least AB doesn't think that). In reality, emotions are what make, guide or break a relationship. You can have a couple who got married with all show-sha still at odds with each other and end up divorced and you have a couple who run away and get married in a court having long happy relationships. If we go by your logic, no person whose engagement got broken would ever get married again in the world. But in the grand scheme of things, these stupid rituals absolutely mean zilch. You can choose to be hung up on them and waste your life and bandwidth arguing with people that they do but people and life move on.
Now coming to his fight for love part,
His actions towards AK (only AK, not AR because that was a deal) might be questionable but his emotions never were. The guy conveys his love and pain through his eyes and everyone other than the AR (even the G clan) could see that or sense that.
Abhimanyu really didn't give 2 hoots to families so winning their approval wasn't a difficulty for him. What was difficult was not able to be with his love AK because she gave all the hoots. So he stood with her and her way of doing things. But he didn't have to do any Maine Pyaar Kiya stunt I agree. The man is honest to a fault. He was ready to talk and convince (never got a chance to do that) but not get a personality transplant (because that's plain dishonesty that's not who you really are).
He was just being himself in front of them a doctor and a lover. The Goenka's we're convinced because they saw his sincerity not because he changed for them. They accepted him as he is. BP even said "He is different from other people but he is not wrong"
I know fighting or convincing family might look really grand on screen but in reality, those people are non-entities in a lifetime relationship. If you change yourself for these external reasons you are being dishonest with yourself and them because old habits die hard. You will be back to your habits and they would be back to disapproving of you. It's better that they like you for who you are and that you start your relationship with complete honesty.
In conclusion, he fought (maybe not as grandly as Prem or any other unrealistic Bollywood hero) not against the family but always against his beloved and for his love. This is harder. His love was tested time and again by no one other than Akshara and he passed with flying colors every time. It's how you can fight for your partner and for your love even when things are bad that makes you a real partner/lover.
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