Virat is reminiscing the happy memories from his childhood, on the banks of the river, and almost naturally, asks Sai to join him for a trip to the place.
You are bang on with the usage of the word 'affinity'. He is reconnecting with his happy childhood with Sai and that is why wants her to join him. He is not asking her for going on a date as she is not a 'woman' yet for him.
However, the moment the words are out of his mouth and he sees Sai's expressions, he realises something and at once tries to put his statement in a context: Something like "tumhaare Aaba bhi tumhe sheher ghumana chahte the."
Sai's inherent question was 'kis rishtey se aau mei aap ke sath?' as there is no rishta as per Virat's words. Bande ko pata bhi nahi hai ke rishta ban chuka hai. Sai is kind of prodding him to be truthful to his developing feelings towards her. Lekin bandene ko kuchh samaza nahi, he went on a backfoot and blurted out 'Aaba' and 'zimmedari' cliche.
I loved you POV.👍🏼