Objection 1. It would seem that one ought not to dispute with unbelievers in public. For the Apostle says (2 Timothy 2:14): "Contend not in words, for it is to no profit, but to the subverting of the hearers." But it is impossible to dispute with unbelievers publicly without contending in words. Therefore one ought not to dispute publicly with unbelievers.
Objection 2. Further, the law of Martianus Augustus confirmed by the canons [De Sum. Trin. Cod. lib. i, leg. Nemo] expresses itself thus: "It is an insult to the judgment of the most religious synod, if anyone ventures to debate or dispute in public about matters which have once been judged and disposed of." Now all matters of faith have been decided by the holy councils. Therefore it is an insult to the councils, and consequently a grave sin to presume to dispute in public about matters of faith.
Objection 3. Further, disputations are conducted by means of arguments. But an argument is a reason in settlement of a dubious matter: whereas things that are of faith, being most certain, ought not to be a matter of doubt. Therefore one ought not to dispute in public about matters of faith.
On the contrary, It is written (Acts 9:22-29) that "Saul increased much more in strength, and confounded the Jews," and that "he spoke... to the gentiles and disputed with the Greeks."
I answer that, In disputing about the faith, two things must be observed: one on the part of the disputant; the other on the part of his hearers. On the part of the disputant, we must consider his intention. For if he were to dispute as though he had doubts about the faith, and did not hold the truth of faith for certain, and as though he intended to probe it with arguments, without doubt he would sin, as being doubtful of the faith and an unbeliever. On the other hand, it is praiseworthy to dispute about the faith in order to confute errors, or for practice.
On the part of the hearers we must consider whether those who hear the disputation are instructed and firm in the faith, or simple and wavering. As to those who are well instructed and firm in the faith, there can be no danger in disputing about the faith in their presence. But as to simple-minded people, we must make a distinction; because either they are provoked and molested by unbelievers, for instance, Jews or heretics, or pagans who strive to corrupt the faith in them, or else they are not subject to provocation in this matter, as in those countries where there are not unbelievers. On the first case it is necessary to dispute in public about the faith, provided there be those who are equal and adapted to the task of confuting errors; since in this way simple people are strengthened in the faith, and unbelievers are deprived of the opportunity to deceive, while if those who ought to withstand the perverters of the truth of faith were silent, this would tend to strengthen error. Hence Gregory says (Pastor. ii, 4): "Even as a thoughtless speech gives rise to error, so does an indiscreet silence leave those in error who might have been instructed." On the other hand, in the second case it is dangerous to dispute in public about the faith, in the presence of simple people, whose faith for this very reason is more firm, that they have never heard anything differing from what they believe. Hence it is not expedient for them to hear what unbelievers have to say against the faith.
Reply to Objection 1. The Apostle does not entirely forbid disputations, but such as are inordinate, and consist of contentious words rather than of sound speeches.
Reply to Objection 2. That law forbade those public disputations about the faith, which arise from doubting the faith, but not those which are for the safeguarding thereof.
Reply to Objection 3. One ought to dispute about matters of faith, not as though one doubted about them, but in order to make the truth known, and to confute errors. For, in order to confirm the faith, it is necessary sometimes to dispute with unbelievers, sometimes by defending the faith, according to 1 Peter 3:15: "Being ready always to satisfy everyone that asketh you a reason of that hope and faith which is in you [Vulgate: 'Of that hope which is in you' St. Thomas' reading is apparently taken from Bede]." Sometimes again, it is necessary, in order to convince those who are in error, according to Titus 1:9: "That he may be able to exhort in sound doctrine and to convince the gainsayers."
Source: Summa Theologica (New Advent)