One thing to bear in mind is that when we are confronted with an uncomfortable truth of any kind, a common initial reaction is denial, then anger, then (eventually) acceptance. No doubt I've missed some stages out there! I don't know what you were arguing about, but whatever it was, maybe in their own time they'll one day get beyond the initial stages of denial (and perhaps face-saving) and think about your reasoning in private when they feel safer letting down their defensive reflex.
Yep, this is how I see it. Although I must admit that during that time of denial my patience is limited after a certain point.
Then again I know I do this, I feel all 3 stages, some I feel stuck in stage 1 still. Stage 1 often takes time to move beyond. But eventually I know I will get there.
Maybe the arguments against Islam simply highlighted a position I had already subconciously reasoned myself into, and the arguments gave me what I needed to make that a waking reality I was prepared to accept. There was a time in my life though, in which I am sure even I would have reacted negatively to the truth of things when it came to Islam.
I still react negatively sometimes to truths I find difficult to deal with, its a process of learning to let go and it takes awhile.