A person once rudely asked that show , where in Qur’aan Allah has said to mourn for the Ahlulbayt (s). I, for now replied to this person that from where in Qur’aan is it written that one should pray taraveeh?

But my real question is what would you answer to him?

With regard to your last question , tell him that Prophet Mohammad (ص), mourned for Imam Hussain (ع) before his shahadat, and this is clearly narrated in Sunni books.
As for his question, you can ask him also for a verse in Quran that talks about how to pray, or how to perform haj …etc.