I would say it is a mixture of apprehension at bringing out his past, which he finds painful even till this day, as well as fear at avni's reaction when he tells her he was in love with another girl. He knows avni too well to know by now that it would make her more unsure about her position in his life if he told her about his first love, juhi, considering how much a tubelight she is, she would still feel he is in love with her, especially consdering he left from the puja, because neil would obviously tell her that is why he left the puja, because of juhi.