The first logical mistake Euthyphro makes is “gods disagree on what is holy and unholy” p9, 8a5-8. Euthyphro tells Socrates that “what is agreeable to the gods is holy, and what is not agreeable to them is unholy” p8, 6e14-7a1. Euthyphro says this because this makes logical sense to him. Once Socrates delves deeper into the statement it becomes less of a straight-forward answer. Socrates says “So by this argument, Euthyphro, the same things would be both holy and unholy” p9, 8a10-12, and Euthyphro agrees.
The second mistake Euthyphro makes is “The holy is what is loved by all the gods” p9, 8a5-8. This is a difficult statement to stand behind because the opinions of the god’s differ