Why does everyone love Alcibiades?

I do not think everyone loved him. He changes his allegiance several times actually. The stuff with Socrates is historically more than debatable (i mean the part about rescuing him).

He is an aristocratic romantic hero, your typical Byronic type. I think if you were an ordinary Athenian citizen you would have voted to exile him just as they did. Like most aristocrats he thought he was born to rule, and this was just after the Tyranny. His widely suspected involvement in disfiguring the Herms is exactly what we have learned to expect of over-privileged upper-class yobs. Even the supposed incident with Socrates can only be thought of as mockery, Socrates was notoriously ugly, showed no sexual interest in his youthful followers and Alcibiades was well over the age when such relationships were considered acceptable in Athens of the time. His wife tried to divorce him because of his relationships with courtesans.

That he was a talented general is certainly true, but his only loyalty was to himself. In a later age he might have been a famous condottieri selling his sword to the highest bidder. He betrayed Athens to the Spartans, the Spartans to the Persians, the Persians by defecting back to Athens. Although Pericles was one of his childhood guardians he was always associated with the conservative oligarchs and clearly proud of his Alcmaeonid ancestry. No wonder that many suspected he wanted to be Tyrant of Athens.

Despite his undoubted charm he seems to have always fallen out with the people whose support he needed. I suspect because he felt they were inferior to his genius. He might have been right, he was the better general than most of them, but he clearly did not have a diplomatic way of putting it. Also one might note even from his youth his reputation for unruly behaviour, which would not have gone down well in the centres of power.

I rather like Aristophanes' take on Alcibiades -

It's most unwise for city states

To raise a lion within their gates:

But if they do, they'll find it pays

To tolerate his little ways.

From The Frogs.