Every apologist is bound to get the question, "Why should I believe that?"
Sometimes the answer is as simple as: "Because the Bible says it," or "Because it follows logically."
But not everyone one meets shares one's common epistemic foundation. Not everyone accepts that logical deduction provides truth. Not everyone believes the Bible. What can we do then?
1. In some cases we can find some other common foundation.
For example, suppose we are addressing someone who accepts only the gospels, and not the other parts of the Bible. In that case, we may be able to prove our doctrine to them out of the gospels. If someone is unwilling to accept the Bible as true, we may be able to prove our point from shared intuition or some other aspect of creation.
2. In some cases we can present our case in a different way.
If a lack of common foundation prohibits strictly logical dialog, we can still discuss the matter using some other mode of discussion. For example, if a person refuses to accept absolute truth, one can appeal to their conscience, to their common sense, etc.
Bottom Line: Some Things are not Arguable
You cannot prove logic's validity logically. You cannot prove to people that the Gospel is true. You cannot cure congenital blindness, you cannot heal leprosy, and you cannot raise the dead. That's God's turf.
You cannot argue anyone to Christ. You can present the truth to them. You can defend the truth against their attacks, but you cannot force someone to believe, whether by sword, by love, by deceit, or by logic. We have to present the truth to people as best we can, and pray to God to open their eyes and hearts and minds to the truth.
May God do so!