Socrates should have drank the hemlock because according to Socrates death is nothing but the separation between body and soul. "To be dead is the completion of this; when the soul exists in herself, and is released from the body and the body is released from the soul." Socrates simply believed that if he died he could grow more as a soul and learn more things that not any living person can learn. Socrates believed that the human body was an endless trouble and didn't want to bear it anymore. He also drank the hemlock because Socrates did not believe he committed any crime at all which is also why he did not leave jail. Once he left jail he would then be a criminal and confirm all the peoples beliefs that he was rightfully convicted, which he wasn't. So by drinking the hemlock, he proved that he wouldn't be lowered the his accusers level.
By drinking the Hemlock, Socrates submits to the demands of the clearly biased jury. He spends the majority of his apology (or greek apologia meaning debate) calling out the ulterior motives of the jury and condescending their insecurities, and yet takes the fall without a fight. By doing so, he subliminally convicts himself of a crime he didn't commit
"Then my good friend, we must not think so much of what the many will say of us; we must think of what the one man who understands justice and injustice, the truth itself will say of us." For a man who believes in the power of the truth, and the understanding of justice and injustice, Socrates gave up pretty easily. if he truly committed to ideals, he would've stood for justice, and truth, not false accusations cast upon him.
Yes,you are right in saying that Socrates tries to persuade people to believe in themselves and be more true to themselves then not how others tell them to be. But he is saying that you should believe the truth not what people tell you because it could be a lie.Such as the cave picture when people are constantly being deceived by what the city of Athens is trying to bestow on people. Socrates believed in teaching the youth and making them realize that they have heard lies their entire lives by asking them questions and making them think for themselves,something that back in the day was not considered a just law. Socrates also gave a fight by explaining his story and that everyone is being deceived and there is a world and truth out there, he tries to show people this but failed to during the jury. Socrates would not escape, to him if he was convicted during the trial then it was over because he wouldn't escape. Only by escaping would he be a criminal, thus confirming their accusations.
Was Socrates really taking a fall? Was he really devoting himself to justice and the cause? Or, was he so overwhelmed by the hypocrisy and the hierarchy involved in Greek Politics that he made the jaded decision to throw his life away? Socrates states " I am far advanced in years, as you may perceive, and not far from death." He goes on to say " I am old, and move slowly, and the slower runner has overtaken me, and my accusers are keen and quick, and the faster runner who is unrighteousness has overtaken them." so, if "they" are the unrighteous ones, how could he possibly "fall on his knees" before them without forsaking his own ideals? He clearly doesn't agree with their idea of what he has done so wrong, so what reason does he have to uphold their unjust system of justice? He bashes their ideals, condescends their authority, and yet he is above escaping their punishment in rebellion?