Drinking the Hemlock was his sentence, not his suicide.

He decided that accepting his sentence was the right and good thing to do and therefore did.

Read up on [link|http://plato.evansville.edu/texts/jowett/phaedo15.htm|Plato's Dialogues]. That's the account of Socrates death. See also [link|http://plato-dialogues.org/tetra_3/tetra_3.htm#case|this page] about Plato's writings.

Socrates was tried and convicted of "impiety" and sentenced to death. He could have saved his life by escaping but chose not to:

Because Socrates was accused of impiety, as a prelude to the trial itself, Plato confronts his understanding of piety with that of one of the upholders of Athenian religion, a sort of seer supposed to be an expert on religious matters, who goes by the name of Euthyphro and happens to have some business in court at the same time as Socrates. And to show how far from corrupting the city Socrates is, Plato shows us how, after his trial, he prefers to lose his life by virtue of a lawful, though unjust, condemnation, rather than making fun of the law by fleeing away with the help of friends.


He DID believe his words, and that is precisely WHY he chose to drink the poison versus escaping.