She couldn't deny it.
She loved.
Loved Pegasus, his Holy, your protector with all its forces. not as a brother, but as the love of your life.
Of course, repeated embodiments, as she doesn't develop something for him? he almost if kill it!
By it was able to bring the moon to it from she asked. and she knows that is not only by loyalty.
Athena know, the two love each other, it and Pegasus love each other, the daughter of Zeus and Pegasus mythology love each other.
But this is a sin... human and gods can not related.
En fact could not, in addition to being a sin it would be breaking your vote chastity to stay pure forever.
But in hindsight... she's broken several rules... almost was a rebel, done everything to protect the Earth and your loved ones human, and love... what love is the worst disease all... do you goes nuts for fault this disease, but this disease... It's worth lose everything for her because she loved one.
Saori Kido, Athena, loved Seiya of Pegasus.
And nothing to do change your mind.