Anurag has always been shown to be a person who stood by Prerna even when they were just known to type friends in Naveen Babu track and till today he took a stand for her whenever needed. Except for Komolika track where although his ways weren't justified but his intention were always to protect her. Even in vikrant case he supported her openly.
Now that they're in love they have a kind of right on each other. A right which you get when you love someone deeply without any pretention. He was planning to get married to her and after all their romantic moments and promises, suddenly he comes face to face with reality. He definitely deserves answers to his questions as he has the right to know.
Her silence brings out the worst of his behaviour but being a person he actually is... He realises his mistake and apologises. Not being able to get answers to his questions he is trying to figure out whatever reason his vulnerable mind can think of. He won't think from heart right now as his heart is broken so he would prefer to use his mind. And in such situations mostly mind wins over heart and so he is trying to win her back.
He is trying to win his love back.... love that belongs to him and which is his right.
'Pyaar apne saath kuchh haq le aata hai jinka ehsaas tab hota hai jab wo humse door chala jaata hai. '