Anyways, awesome analysis... totally agree...
They are both right in their places... and your title says it all... both care... Khushi hugged him back, and Arnav stopped when Khushi asked him to... we all know what ASR is capable of... he could've forced her... he didn't... she could've pushed him away she didn't...
They've both grown up with their beliefs and underlying insecurities...
ASR has lost loved ones... he's insecure with that... remember, he asks Anji Di "aap mujhe maa ki tarah chod ke to nahi chale jaaoge na???" that is the insecure boy beneath that arrogant man... he can't let Khushi go... he loves her... and he depends on her... emotionally, i mean... he's started sharing his past, his problems with her... do we know ASR to do that??? so, of course he's changed for his love... but in his own way... and we don't need anymore changes because as you said... he won't be ASR anymore...
For him, rituals have never mattered... feelings have... is it such a wrong notion to hold...?? that feelings are more important than rituals... he has accepted her as a wife... giving her all the rights of one... she's legally married... the society have accepted the relationship... its not that he's keeping her insecure from any angle... so, why blame him?? they are not in a live-in... they are a married couple for everyone INCLUDING ASR... so for him all the rituals hold no meaning... for him its just a show... and if Khushi had asked him for a remarriage he would have obliged... will he ever deny Khushi anything??? but at that moment he just wanted to express his love and make Khushi his in everyway to eliminate all the insecurities... and i haven't yet figured dadi into the equation... remember her??? Arnav knows her well! come on! he gets his gene pool from that woman... so, he knows, if anything happens she would try to separate them... which he is against... she is rubbing his past on him... which he is wanting to let go... do we need anymore proof that is is primal in its most basic respect... so, yeah... she is a threat... and a bigger one than our snake because she has power and authority over this family...
Coming to khushi, she is a girl - small town Indian girl... do you require anymore explanation??? she has grown up with the beliefs that for a girl marriage and husbnad matter the most... Now, don't go about saying she should've then respected Arnav's decision... why? don't you want her taking her stand??? and, anyways... I said marriage and husband... and there can be no husband without a proper marriage, can there??? what Arhi had wasn't marriage... forget the rasms and pheres... even when he made her wear Sindoor and mangalsutra, it wasn't with any of their consent... Arnav was forced by circumstances and Khushi was forced by Arnav... nothing pious about that, was there??
Another point, the kind of man Arnav is "Pal mein shaitan pal mein rajkumar" with such mysteries revolving around his actions... the girl is bound to be insecure... she can never predict him... and this aspect frighten's her at a level... what if one day Arnav decides that he's had enough, he doesn't want Khushi in his life... we know that'll never happen... but does Khushi??? he'll say we didn't even have a proper marriage... and now i don't want you... what will khushi do?? she'd have no refuge... because thats what her beliefs are going to say... you didn't have any proper marriage... and then she'll feel like a used s**t... is this what we want?? hell, no! comeon uptil now Arnav had just said "I Love You" once in a life threatening situation... At that time for Khushi how'd it translated?? Arnavji is in danger... why??? because the girl couldn't believe that the man who tortured her at so many levels... accused her of being characterless and cheap said "I love you"... insecurities... she didn't know Arnav's intentions then... if Arnav had asked her at that time or even brought his Di into the equation and said You'll have to marry me because of Di... his husband is lusting on you... would Khushi have refused?? no again! but he didn't... and hence the insecurity... and for her every cute romantic moment they shared was some dream she was living... she herself said "whenever i start to forget about you, you remind me of your inhuman ways"... so she is scared of that... until when he finally said in the heat of the moment that he does love her ofcourse... and the more Khushi starts to believe in those words... the more reality will set in...
So, both are right... both care for the other... but both are failing to figure the other person's insecurities... that happens in any relationship... so there's no need to bash anyone... both characters take their own ground... and that is the reason we love them! whats Arhi without their fights???