it ain't an opinion, caitlyn jenner is a woman.
While I support trans people and such, this is kind of a bad argument
In his mind, a woman is someone with a vagina. You two have different beliefs on what womanhood is. Calling it a fact won't change anything because it's not really a fact, it's semantics.
I would just say why does it matter to you if she identifies as a female?
How does it affect your life? Surely if someone would take such a huge risk (serious cosmetic surgery + being the 'icebreaker' for trans people in mainstream culture + being in the public eye during all of this) to recreate themselves there's a legitimate reason for it.
It's simply a matter of politeness. If someone feels that they are not cisgendered it's no skin off your back to treat them as such.
And unlike identifying as a carrot, gender dysphoria has legitimate roots in psychology and biology. It is recognized as a mental state (NOT a disorder) by the American Psychological Association. Studies have found differences in the brain structure of trans people and cis people.