Heracles is supposed to be an ideal Greek man. Despite this, he murders multiple people, kills his own kids, abducts Iole, and possibly cheats on Deianira. How did Greek listeners understand these events and promote these stories as part of proper masculinity?

Hercules was viewed as the ideal man only in the sense that he transcended humanity.

Greek heroes were not, as a general rule, morally admirable. They were simply mortals who had achieved something remarkable in life, and deserved lasting recognition in death. Like any Greek hero, Hercules pushed the bounds of human possibility, and was in that sense admirable. He was remembered, moreover, as (what we would call) a "culture hero" - someone who prepared the way for civilization by destroying monsters.

Even myths that presented him in a positive light, however, never ignored the collateral damage Hercules tended to inflict on the communities he helped. He was usually described as more or less well-meaning, if a bit dim; but even when Hera wasn't driving him to atrocities like the murder of his children, he had a murderous temper that often led him to destroy some or all of those he had set out to help. Unlike, say, Theseus, he was very much a "stab first and ask questions later" sort of hero.

But the Greeks admired his deeds, not his character. And since, uniquely among Greek heroes, Hercules became a god upon his death/apotheosis, he was revered as a patron of mortals, especially those with a special interest in health and physical strength. Shrines of Hercules could be found in every Gymnasium, and athletes sought his blessings before competitions.

Hercules is a strikingly protean figure in Greek literature. Sometimes - as in Euripides' Alcestis - he appears more or less as he does in the myths: immensely strong, crude in manner, and none too bright. But as early as the fifth century BCE, he began to also be presented as a proto-philosopher - probably because (as a mortal who became divine) he was a natural metaphor for the perfectibility of mankind. This is the origin of the famous "Choice of Hercules" myth, first outlined by the sophist Prodicus: a young Hercules encounters two women - Vice and Virtue (or in other versions, Good Order and Tyranny); Vice offers him riches and fame, Virtue promises hardships in the service of the good - and Hercules wisely chooses the path of Virtue.

In the end, as a mortal who became a god, Hercules was simply a familiar figure who could ethicized as needed to fit a given author's purposes. This interpretation, however, always co-existed with myths in which he was admirable, if at all, as an avatar of brute force.