When engaging in a "discussion" or "debate" or "dialogue" with someone not of the Catholic faith, I think there is one especially important thing to keep in mind - if you don't know the answer to a question, or if you just aren't sure how to respond accurately - for Heaven's sake don't TRY and answer it off the top of your head! More often than not whoever you are talking to will seize on this error and use it to his advantage. In the long run it will weaken not only your cause but the cause of the Church.
The truly beautiful thing about the Catholic faith is that we do have the answers. Personally we may not know everything there is to know, but if you look hard enough you can find what you're looking for. If a question is asked of you and you are not sure how to respond, simply say, "I can't answer that right now but if you give me a little time I will get back to you." No harm done.
Nobody has complete knowledge of their faith. However strongly you may disagree with someone, if you cannot answer the argument with a sound, justified answer of your own, don't answer at all. Ask for time and get back to the person. Use prudence.
When the current situation you face is less in the realm of apologetics and more of evangelization, keep these words of C.S. Lewis in mind:
Ever since I became a Christian I have thought that the best, perhaps the only, service I could do for my unbelieving neighbours was to explain and defend the belief that has been common to nearly all Christians at all times. I had more than one reason for thinking this. In the first place, the questions which divide Christians from one another often involve points of high Theology or even of ecclesiastical history, which ought never to be treated exept by real experts. . . And secondly, I think we must admit that the discussion of these disputed points has no tendency at all to bring an outsider into the Christian fold. . .Our divisions should never be discussed except in the presence of those who have already come to believe that there is one God and that Jesus Christ is His only Son.I believe we must first simply lead unbelievers to God, and then hopefully to the Catholic Church. If the person you are engaged with is truly seeking the truth, how else can he end up any where but the Church?
- from the preface to Mere Christianity