Alcibiades asserts that Socrates pretends to be erotically attracted to younger men and to be completely ignorant, but that these are all covers. In fact, he lives with great moderation, is very wise, and has no interest in bodily concerns. Once Alcibiades became aware of Socrates' great wisdom, he hoped to seduce Socrates with his good looks in order to glean some wisdom from him. But when he finds himself alone with Socrates, Socrates just converses with him as he always does, not making any kinds of advances. On one occasion, he went with Socrates to the gymnasium and they wrestled together, alone, but Socrates still made no advances.
Finally, Alcibiades gave up on waiting for Socrates to make an advance and started actively pursuing him. He invited Socrates to dinner on several occasions, and once they stayed up talking so late that Alcibiades was able to convince Socrates to stay the night.
Alcibiades pauses here to note that he would not go on were he not so drunk. Like someone who has been bitten by a snake, Alcibiades has been bitten by philosophy, but since everyone else here has also been bitten, he feels comfortable sharing his story.
Once Socrates and Alcibiades had rested themselves upon the couches, Alcibiades put it straight to Socrates, telling him that Socrates was the only lover good enough for him and that he would gratify Socrates in any way he wished if Socrates would help to make him a better person. Socrates replied that if things were as Alcibiades had put them, Socrates would be getting the short end of the stick, exchanging deep wisdom for cheap thrills.
Alcibiades joined Socrates under one sheet but by the end of the night, Alcibiades had not managed to arouse Socrates in the least. Alcibiades felt humiliated, but admired Socrates' self-control. He found further evidence of Socrates' admirable qualities when the two served together in a siege against Potidaea. Socrates was better than all the others at putting up with food shortages and with the winter, and when there was a feast, Socrates could drink everyone under the table without even getting tipsy. On one occasion, Socrates spent an entire day and night standing still, thinking about a problem. In battle, Socrates showed great bravery, once saving Alcibiades' life.
Alcibiades concludes his speech by remarking that we cannot liken Socrates to any other person, past or present. At best, we can compare him to a satyr who is god-like on the inside. Alcibiades warns Agathon not to be fooled or seduced by Socrates in the way he has been.
You do not have to look outside you as everything is in your "self", everybody is the two energies (woman-man/yin-yang/...) and if you awaken your "opposite" you are "one", you are realized, totally happy. This is called e.g. in the Bible the Holy or Mystic Marriage. Also the alchemists describe it as "Coniunctio Oppositorum", the Philosopher's Stone, make Gold from Lead,... See the writings of the Mystics too. Etc.