The offense of the gospel is that it is good news!

The gospel is meant to be an offense to religious people... not to sinners!  The gospel really is good news for sinners.  "God demonstrates His love for us in that while we were still sinners, Christ died for us."  "Christ Jesus came into the world to save sinners."

There previously was an old covenant through which sinners were condemned.  The law stood to make the whole world guilty before God.  It was the ministry of death and the ministry of condemnation (2 Cor 3:7-11).  It was not good news.  It was bad news.  It was the ministry the Apostle Paul had formerly preached vehemently.  The ministry of the good news had been offensive to Paul.  It had been enough of an offense to him that he went around persecuting and killing those of the Good News way.

But then Paul came to understand that the good news really was good news, and that Christ had come to deliver us from the law and from condemnation.  Paul then stopped preaching the bad news and he stopped persecuting those who believed the good news, and he himself became a passionate preacher of the good news.  Those in Judea said of Paul, "He who formerly persecuted us now preaches the faith which he once tried to destroy."

So Paul had formerly been a deeply religious legalist, rooted and grounded in the bad-news ways of the Old Covenant.  In his letter to the Philippians, Paul told them all about this.  He talked about his Jewish heritage, and how he had even considered himself blameless according to the law!  That was his life.  That's the "news" that he had lived by.  In his blindness, he didn't see that it was bad news.  But then when he began to "see," he found that he had to chuck all of that aside and count it all as dung (his own words) so that He could be established in the good news of grace and peace, and of forgiveness of sins, and of the Lamb of God who took away the sin of the world.

And that is what offended people!  Paul, the former persecutor, began to be among the persecuted, all because he stopped trusting in the law and the ways of the Old Covenant and he began trusting solely in the finished work of Christ and the gift of righteousness by grace through faith.  He began telling "sinners" that God was in Christ reconciling the world to Himself, not counting people's sins against them (2 Cor 5:19).  That message had previously infuriated him, and now he was in the business of laboring hard (by the grace of God) to spread that very message.

It's a "good news" message in every way.  The good news message is an offense to those who are of the law - and even to those who say they believe in Christ and yet want to add works, rules and laws to faith.  But to anyone and everyone else - to sinners of every kind - the good news is meant to be a beautiful and joyous sight and experience!