May be true... however many brilliant Christian apologists (logical theologists) will admit that logic never saved anyone. I used to think there was merit in arguing/debating with people about this. But I realized through some frustration this is just not the case at all.
John 6:44: "No one can come to me unless the Father who sent me draws them to me..." -Jesus
So faith is a gift... not something to be argued, debated, or proven. It can't be transferred from human to human. It is a free gift, given to those who will accept it. If I accept it and you accept it, it is not our job nor is it beneficial to anyone for us to argue with those who knowingly choose not to accept it.
That said, you have my respect for keeping your cool. I know it's not easy.