I really don't think you have anything to be embarrassed about.
The friend that pointed out that it's all about her preference, comfort and desires is, in my opinion, speaking honestly, but her honesty was honed by what's accepted/not accepted by current society. She doesn't know any better.
I truly believe it all boils down to what people are programmed to believe and accept. We live in a world where, for the most part, only two sexes are recognized. Therefore, only two genders are recognized. And consequently, gender must match sex.
But if the binary theory were to stop being crammed down peoples' throats from the day they were born, and people accepted and recognized that any variation and combination of sexes and genders are possible and normal, when a person's gender discord or variance came to light, it would be looked upon as just another change in one's life that simply needs incorporating into any relationship, whether familial, intimate or social.
Hence, "no big deal."
P.S. Bashing not allowed.