Tell me something about Gallio who is mentioned in Acts 18:12. Why don't people care about what Christians have to say? Why don't Christians care about the lost as they should?
"But when Gallio was proconsul of Achaia, the Jews with one accord rose up against Paul and brought him before the judgment seat, saying, "This man persuades men to worship God contrary to the law." But when Paul was about to open his mouth, Gallio said to the Jews, "If indeed it were a matter of wrong or of wicked crime, you Jews, it would be reasonable that I should bear with you; but if they are questions about words and names and your own law, look to it yourselves. For I don't want to be a judge of these matters." He drove them from the judgment seat. Then all the Greeks laid hold on Sosthenes, the ruler of the synagogue, and beat him before the judgment seat. Gallio didn't care about any of these things" (Acts 18:12-17).
According to Adam Clarke, "This deputy, or proconsul, was the eldest brother to the celebrated Lucius Annaeus Seneca, the stoic philosopher, preceptor of Nero, and who is so well known among the learned by his works. The name of Gallio, was at first Marcus Annaeus Novatus; but, having been adopted in the family of Gallio, he took the name of Lucius Junius Gallio. He, and Annaeus Mela his brother, father of the poet Lucan, shared in the disgrace of their brother Seneca; and by this tyrant, Nero, whose early years were so promising, the three brothers were put to death; see Tacitus, Annal. lib. xv. 70, and xvi. 17. It was to this Gallio that Seneca dedicates his book De Ira." Albert Barnes also states, "He is described by ancient writers as having been of a remarkably mild and amiable disposition. His brother Seneca (Pref. Quest. Natu. 4) describes him as being of the most lovely temper: "No mortal," says he, "was ever so mild to anyone, as he was to all; and in him there was such a natural power of goodness, that there was no semblance of art or dissimulation.""
If such is the case, it appears that the Jews had managed to irritate Gallio quite a bit. When they brought Paul in on charges that he was persuading people to worship in a manner contrary to their law. Gallio didn't even let Paul make a defense; instead, Gallio turned on accusers and threw the case out of his court. The problem was that he is a Roman official overseeing a Greek district and here he as people from a different province complaining about religious arguments over their obscure (from Gallio's point of view) law. He bluntly told them he didn't care about their law.
What is surprising is that some Greeks in the court started beating the ruler of the local synagogue, right in front of Gallio, and he chose to ignore it. As I said, apparently the Jews hadn't endeared themselves to the Romans or the Greeks in this area.
This is not about people not listening to Christians or Christians not teaching the lost. This is about the enmity that existed between the Roman government and the Jews. The result was that the Jews in that area were unable to hinder the spread of the Gospel by using the government to be their strong arm. Therefore, Paul stayed for a while in the area to teach (Acts 18:18).