Apologetics can be a loaded term as it encompasses so much in the way of history, theology, philosophy, science, and archaeology. Many in the church make the claim that Jesus did not use apologetics, so why should we. But this is not the case.
For an illustration, let's take a look at Jesus pointing out a Self-Refuting argument.
In Matthew 12:22-28, we read about Jesus casting out a demon and the following exchange:
22Then a demon-oppressed man who was blind and mute was brought to him, and he healed him, so that the man spoke and saw. 23 And all the people were amazed, and said, “Can this be the Son of David?”24 But when the Pharisees heard it, they said, “It is only by Beelzebul, the prince of demons, that this man casts out demons.” 25 Knowing their thoughts, he said to them, “Every kingdom divided against itself is laid waste, and no city or house divided against itself will stand. 26 And if Satan casts out Satan, he is divided against himself. How then will his kingdom stand? 27 And if I cast out demons by Beelzebul, by whom do your sons cast them out? Therefore they will be your judges. 28 But if it is by the Spirit of God that I cast out demons, then the kingdom of God has come upon you.
Here, Jesus points out a clear logical fallacy committed by the Pharisees. In today's world, people still do the same thing. How often have you heard someone talk about speaking "their truth" or "that's true for you, but not for me"?
By asking questions the way Jesus did, we can point out the problems with these views to help bring a better understanding of the nature of truth and in so doing, bring someone closer to being ready to hear the Gospel.
Jesus used arguments and we should too.