 Of course Achilles wasn't bisexual. We don't even know if Achilles and Patroclus actually existed. Maybe they were just a myth, but did the writer of the Iliad intend them to be bisexual? Well, we don't know who wrote the Iliad. Was it passed along? Did Homer write it? Was Homer even an actual person? But the reason we still know about Achilles today is that the Greeks in the 5th century BC discussed so much about these stories. And they absolutely believed Achilles and Patroclus were lovers. Because that was the norm in their society. But that doesn't mean the norm was to be bisexual. Bisexuality is a modern invention, an identity we use to label ourselves and others based on sexual preference. But it doesn't make any sense to transpose that label back in time. So even though Achilles and Patroclus were lovers in the story as it was given to us,