Euthyphro is overconfidence about his knowledge,so Socrates seeks knowledge from Euthyphro since he is facing charges of impiety, thinking he may learn to defend himself in his own trail. he then expresses his thought on how the gods are cruel and inconsistency, which lead him to ask Euthyphro to define "piety" (moral correctness or truth). but with every definition he find a flaw which leads to Socrates not learning anything that will help him defend himself in his trial.

why socrates thinks he is wiser?

Socrates think he is not the wisest person out their,so to prove his theory he set out on a quest to find a person who is wiser than himself. First he went to the politician who he began to ask question, but only to find out that the politician was not as wise as they think. then he went to the poets where he quote some of the most elaborate passages, only to find out that they are the same case as the politician who think as themselves as the wisest but to find out their are not. He then went to the artisans, thinking they might know more since they were workmen. He soon proved that wrong because they were like the others where their own wisdom overshadowed and defect them.so to some his up Socrates is the wisest out of them all and he is better off by himself.