Great question, Kina!
If someone is facing straight at you and you focus on one eye, the other eye will still be in focus because both eyes are in the same plane of focus. If the person is angled so one eye is closer, then you have to choose which eye to focus on, right? What do you do? (Now of course, there are a lot of variables could be talked about that effect how much of the picture is in focus with aperture and focal length and all.)
But this comes down to a subjective question that can be asked of any picture you take: Where do you – the photographer – ultimately want the viewer’s eye to go when they look at the photo? Focus on that.
The reason you want to “focus on the eyes” is because that’s where you want the viewer’s eyes to go. The main point of a picture of a person is not their ear or their mouth (at least I hope not!), it’s their eyes – because that’s where you connect with a person in real life, through eye contact.