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Anon39 Maybe you could get hold of some kind of reading material that discusses the issues. A newspaper (with a liberal editorial policy) might be the most digestible for someone so conservative. There are some amazing short fiction stories. And there is solid academic and scientific research.
I remember when I first heard the idea that there are not just two sexes but astonishing variety in between. Then I heard that there was such a thing as brain-sex being at odds with the sex of the body - literally physiological differences in the way the brain processed and responded to input - not a matter of cultural or familial conditioning and not a result of abuse. I felt shocked and amazed - all my preconceptions had been turned upside down and inside out. It created what psychologists call "cognitive dissonance", a state of discomfort when suddenly what one perceives to be reality turns out to be not fact. It takes time to adjust. For me, one of the easiest ways to do that is to saturate myself in information about the new reality, learn to understand it. At a certain point, something "clicks" and it becomes the new norm for me. I now understand male/female and the spectrums of variation as more like a colour wheel than a black and white binary.
A lot of people do get angry when they get hit by cognitive dissonance. It's partly because most people
identify with their beliefs. For instance, they might think, "I am a Christian" rather than "I live by Christ's teachings." (Not realising that beliefs, roles, jobs, values, goals, etc, can all change, yet one remains the same person). If their beliefs or values are challenged by something that doesn't fit, they feel an emotional reaction as severe as if someone had stuck a knife in their guts and twisted it. The new reality might take quite a long time for them to adjust to. And some simply refuse; they'd rather reject the evidence and hang on to what is comfortable and familiar.
We can't control how others think or feel - and really, we don't have a right to. Influence can occur, but it's the other who decides, not us.
Sadly, you might have to watch your Dad go through this struggle when you're finally ready to come out to him. He might eventually come around and accept you exactly as you are - which would be wonderful. I think nowadays most families do finally adjust and accept.
But whether he does or doesn't, our greatest happiness is always in being true to ourselves.