Being transgendered means that your inner self does not match the physical sex you were born with and sex as determined medically is by the predominant sexual organs.
Many transgendered individuals, myself included, are born inter-sexed or with Disorder of Sexual Development and your friend is a "she", not a "he".
Being transgendered is considered a psychological condition and if you were truly friends you would do research because the party in transition has likely spent the majority of her life in deep depressions with nothing more than looking at the fact the outside doesn't match the inside. Mentally and chemically, she is just as much female as you are perhaps more because she at least had the compassion to be honest with you and you outed her.
It is not uncommon on Hormone Replacement Therapy to be attracted to the opposite sex (which would not make your friend or the transsexual "gay"- since she is a female).
Some form of inter-sex conditions affect as many as 1 in 250 people the most severe cases such as DSD affect 1:2500.
Men often hit on me and I make sure they know that I am transsexual and inter-sexed so to avoid this type of situation. What you did could have likely set this girl up to be beaten, raped or killed so I would certainly not refer to her as a friend. Transgendered are among the highest mortality rate in the LGBT community and much of that is due to homicide.
If your "friends" were attracted to one another there is more to it- try doing research on Kinsey, Freud and many other psychologists and perhaps search the web. If your male friend felt like you set him up then perhaps your issue is that she is more attractive then you and your sister. You might search out pan-sexual for starters.
Edit to comments: Look up the definition of transgendered.
I was born 80% female but my predominant sex determination at birth was male. I had an ovarian testee- am I a male or female, doctor?
Wrong I was determined by a medical doctor to have been born inter-sexed and predominantly female. The doctor at my birth opted to change my sex because it was easier to sew an opening shut then remove an enlarged clitoris. 4 endocrinologists have tested me and I am not on HRT due to family history of breast cancer. How many men do you know born with ovaries?
You may justify your actions as protection but in most cases it is the furthest from the truth and can cause severe harm to a transsexual. By the way XXY is a condition known as Klinefelter's Syndrome- there are many conditions of Disorder of Sexual Development, that one happened to be a misdiagnosis.
EDIT EDIT: You went to medical school and know nothing about Disorder of Sexual Development...are you now claiming you are familiar with this and or being transgendered because most medical schools approach trans-sexuality and require developmental and abnormal psychology as prereq. classes for med. school? I am assuming you mean you are a CNA, X-ray tech or med billing and coding, etc...
and to quote Kindergarten Cop: "boys have penises, girls have vaginas"- this is as far as you got isnt it?