Arguing with Atheists
The Church's teaching that God can be recognized by the right use of reason does not mean that we can convert every atheist we argue with. People have to be willing to be converted in order to let us touch their hearts: "A man hears what he wants to hear and disregards the rest" (Paul Simon, "The Boxer"). God is the changer of hearts. He loves Tomas with His whole mind, with His whole heart, and with all His strength--but He gives His children freedom to resist His Spirit. Those who want to see will see; those who want to hear will hear.
This is one of those many "no rules" situations where all we can do is let OUR conscience be our guide. When we think that we have made the best case that we can for the Catholic vision of reality, then we may rest from the argument with the knowledge that Jesus does not want us to exhaust ourselves in argument with those who are unwilling to be converted and healed.
We have Jesus' sayings about "shaking the dust of those towns from our sandals" and not throwing pearls before swine to assure us that we may, in good conscience, abandon a fruitless argument. Until then, we should be "as cunning as a serpent and as gentle as a dove" in trying to show our opponents what we mean. It could well be that we are the instrument God has chosen to pierce their defenses. There is no way to tell in the abstract. WE get to make the call about how WE conduct ourselves in the conversation. When we have done all that we personally want to do, then we may say, "We'll just have to agree to disagree."