Key verse: "...but was in all points tempted as we are, yet without sin."--Heb.4:15b (NKJV)
In public interaction, you are sometimes misunderstood and confronted about what you have just said. Sometimes, you say something badly and need to quickly rephrase it. On occasion, you realize that you have spoken an inflammatory or inappropriate remark and must make amends.
We observe high profile persons having to apologize for certain words or behavior. During an interview or at a social gathering, a celebrity/athlete/political figure makes a remark or commits a social blunder which angers other people. A retraction or apology is instantly demanded---and usually granted.
Throughout the course of His public ministry, Jesus angered lots of people. In fact, He angered certain people so much they plotted to kill Him. But, He never issued an apology. He never backpedaled on any of His comments; He never became embarrassed or publicly humiliated about His conduct. He never declared: "I'm sorry, I was out of line, it was wrong of me to say that."
This is significant. The Messiah's enemies tried repeatedly to trap Him on the basis of what He said (Matt.22:15-18; Luke 20:26; John 8:4-6). They employed one argument after another in order to discredit Him. They crafted numerous schemes to make Him look awkward in public.
Not once did they succeed.
Scripture presents Jesus as the sinless Son of God. He was without sin, despite being fully human as well as fully Divine. He never apologized to people because He never sinned. And: He never told a lie because He was and is the very Truth of God.
However, the sinless and true Savior died for sinners who would become people of faith in Him. His sacrifice in our place has secured for all believers a place in heaven. Salvation---not a public apology---is what God has given to the people of His Son.
"For He made Him who knew no sin to be sin for us, so that we might become the righteousness of God in Him."---2 Cor.5:21