Hubris was frowned upon in Greek and Roman myth. Icarus' downfall came when he though himself to go where only the gods and heros had gone before. As humans, we have limitations, and Icarus disregarded that knowledge. Keep in mind that, at the time, the sea belonged to Poseidon and the sky belonged to Zeus (no planes or subs, ships yes, but sailors knew that Poseidon ruled them). Had Icarus heeded his father's warning and stayed between both realms, he'd have been safe, but once he crossed that line he lost his life.
Phaethon came to a similar end because of hubris. He thought he could drive his father's chariot because he was the son of a god, he felt that he had to prove that he was better than human, but even the sons of gods had limitations. According to Apollo, Zeus himself wasn't strong enough to pull his chariot or control his horses. Had Phaethon kept to the middle ground, or better yet, stayed out of his father's chariot, he wouldn't have nearly destroyed the earth and been killed in the process.