Socrates and the Sophists had contradictory views on the Truth, which brought them into conflict, and as the Sophists were by far the more popular the the rivals, eventually resulted in the execution of Socrates. Though, not before he shook the Sophist’s from their popular pedestal.
We don’t really know how the Sophists came to their views, but there are some theories. The first theory is that they thought that the absolute Truth was so elusive and impossible to figure out or attain, that there was no real point to trying to find it. And if there isn’t anyway to verify the truth, then you might as well go along in life believing in and practicing in whatever you think will benefit you most, since, after all, who’s to say that isn’t the Truth? The second theory is that they didn’t believe that an absolute Truth existed in the first place, and so you might as well do whatever you wanted to. Or, it’s possible that they believed the the Truth was a subjective thing and that the best thing for yourself was the Truth, at least for you, and at that time.
The Sophists were quite popular, as they would teach the wealthy and the wealthy peoples children rhetoric and public speaking, important skills in ancient Athens. They would also be tremendous suck-ups in order to get more money and popularity, as was in keeping with their “what’s best for me” philosophy. when arguing they would also not care if they were inconsistent, so long as they won that particular argument.
Socrates, on the other hand believed in pretty much the opposite, that Truth is an absolute, incapable of changing, and that it is fully within the powers of man to discover this eternal truth. He was also quite patronizing in his teaching style, first forcing his students to admit that they did not know a thing before guiding them to discovering the answer. And while the Sophists charged money to teach a student, Socrates didn’t, believing learning to be a universal goal that everyone should strive for, regardless of wealth. He also considered everyone who didn’t know a thing that he knew, to be his student, regardless of whether or not they wanted to be.
This all combined to make Socrates a much disliked figure in Athens, and so he was sentenced to death for corrupting the youth with his philosophies. Yes, you read that right, he was sentenced to death for teaching children about objective morality, while the subjective Sophists who believed in doing whatever you wanted, kept on teaching the most powerful of the people. But Socrates did shake their monopoly on Athens, and they were never quite as popular as the were.
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