The word “apology” comes from a Greek word meaning to verbally defend yourself after being accused of something. It involves giving reasons for the behavior as a way to justify it to the accuser.
Sometimes an offended person will claim that hearing the words “I’m sorry” isn’t good enough, so they will tell the offender to “explain yourself”. The offended person is hoping that the reasoning the offender uses in their “apology” will provide a means to effect change in the offender’s attitude when they realize the flaws in their reasoning. The character issues (usually selfishness and/or prideful assumptions about privilege?) revealed in the explanation can be a humbling experience for the offender that can help them “see the light”. This is probably a good way to raise children because it forces them to think about what motivated them so they can provide an explanation. Then the parent can offer some details about how to change their behavior in the future (to repent?).
A Christian should always be ready to give a defense for their beliefs (2Peter 3:15). The reason this is called “apologetics” is because a scoffer (polite or otherwise) is attempting to mock or disavow Christianity as a way to reject their Creator’s efforts to reach them, so the believer must explain the reasoning for their faith in the God of the Bible.
Using apologetics (a reasoned approach to sharing Christianity rather than a mere emotional appeal) can be an effective way to honor the Great Commission (Matt 28:19-20a, Jesus’ command to “make disciples of all nations”). However sometimes a well-intentioned believer will use it to badger a loved one into repentance. Unfortunately, we cannot out-debate a person into accepting Christianity, we can only sow God’s seeds into their minds (Matthew ch 13) and hope that God will call them into a saving relationship. God calls the people He wants, and we are merely the messengers that find and lead those people to Him (Jn 6:44, 2Tim 1:9, Acts 2:38-39, 2Thess 2:13-14). As examples consider Acts 8:26-39 (an angel directs Philip to witness to the curious high-ranking official), Acts 16:23-34 (Paul’s behavior in the jail convinces his jailer to want Christ too), Acts chapter 10 (Cornelius, the first Gentile believer directed by a vision from God to find Peter), Acts 18:1–6 (Paul accepts the Jews rejection of his teaching and declares he will now focus on gentiles) and 2Tim 1:1-6 (Paul mentors Timothy because he saw that Timothy’s heart was prepared by his mother and grandmother). When Jesus sent His Apostles on their first mission He told them that villages that did not accept them should be abandoned (Luke 9:1-5). God also accepted the rejection of His invited guests to the wedding in Luke 14:16-24. He did not harangue them into coming, He invited others instead who happily accepted His offer.
So live in a way that shows Christ’s light being developed in you (1 Peter 2:12, Matthew 5:14-16) so people will see you can be a reference for Him. Be ready to share the truth with any who ask, and gently witness as the Great Commission requires (including apologetics along with personal testimony if you sense that is the way the hearer understands things).
Romans 10:14-15 How, then, can they call on the one they have not believed in? And how can they believe in the one of whom they have not heard? And how can they hear without someone preaching to them? — And how can anyone preach unless THEY ARE SENT? As it is written: “How beautiful are the feet of those who bring good news!