Just a theory of mine: Most people have an "ideal" in their heads about how people and society should be, whether it be from their religion, upbringing, or the media, and they automatically reject anything that doesn't fit that ideal as being bad, evil, or otherwise wrong. I think it's a really deep-rooted psychological thing so it never occurs to them that it isn't backed by an ounce of logic. JMO.

~M

People are afraid of what they don't understand. For the past few months I've been talking to my mom about trans issues because she's absolutely fascinated by it, though at the same time she's somewhat repulsed. It's just so beyond what she was brought up understanding about gender. She wants to "get it" and not be transphobic, but it's hard for her. A documentary came on TV one night, coincidentally, and she found that after watching it she was a bit more comfortable with the idea. For her, it was about normalizing it enough that she could wrap her head around the subject and not just have a knee-jerk reaction of aversion. She still finds the whole thing strange, but there's definitely been progress made, and it's all been about learning individuals' stories and humanizing them so that they can be approached at a level of common ground.

I believe this hate comes from fear, people fear things that are different, they fear things they don't understand. Most of the transphobic people I've met are parents who are afraid that accepting transgender people will make it mainstream and then 'infect' the children. Most of these people are also homophobic for the same reason.
My father actually said that he dislikes the term (trans/homo)-phobia, because it implies fear. "I don't fear them, I just hate them, they're wrong."

I think a lot of people live in very small worlds, at least with regard to sex and gender.

They don't think about these things, they believe the current "system" benefits them or at least they don't see it causing themselves harm.

They don't think about gender and sex as anything more than male or female. They don't think about their own gender expression, or even their own sexuality all that much. They take them for granted and never learn or explore.

And in America, at least, I feel that certain religious ideas do have an impact. I don't believe all religious people are transphobic or bad ! It's just an attitude that comes with a certain kind of faith that says it is your personal job to make sure people are on the right path. I know religious people who are NOT like that, but unfortunately some are and are vocal about it, telling people that they must live a certain way because their interpretation of scripture or personal norms dictate it (and certainly, non-religious people can be guilty of this as well).

People really don't get it. The things I hear come out of people's mouths when trying to explain why transgender people are "wrong" show such appalling ignorance, it's scary.

I think it's mostly because people don't like change.

HAHAHA GOOD QUESTION, TRYING TO FIND THE ANSWER TO THIS ONE MYSELF ACTUALLY!

But in all seriousness, my therapist told me that it's because people use gender as a means to understand people, and when something challenges their views on gender, they get confused and fussy.

I would guess that most of it stems from confusion and lack of ability to understand or connect. A lot of people very strongly identify with their sex as their gender, and find it very hard to separate the two. Whenever sex and gender aren't linked, the first reaction is confusion, and then it moves on to being defensive. A lot of people have a very strong urge to view themselves as what is "normal", and what deviates from that is either not right, or is a judgement passed personally against them. Add in confusion from people who weren't specifically transphobic as to how they're supposed to address someone who is trans... and then there's people assuming that transpeople are taking attention away from "rightful" issues (read as their own personal sexuality-based agenda).

I sometimes wonder if the view I was taught on transsexuals and transgenders was phobic... my father taught me that it's caused by different formations of brain and hormones, and that it must be very frustrating and painful for individuals affected to have a mind and body that don't quite link up. He asks after my trans friends and always remembers to address them by their proper pronouns, but I've heard his biological reasoning is insensitive. I'm not quite sure where I stand on the first part, but I do agree on the second.

People tend to hate and fear what they don't understand.

In general, people will also take just about any excuse to hate someone else for their differences. At least that's what I've observed.

Just briefly, the main reason that I see for it is that people are mostly raised to believe in the gender binary, that everyone can be classified as either male or female, and nothing else. So then when they discover the existence of trans and intersex people (who challenge the existence of the gender binary), this can annoy a lot of people because it makes their gender identity seem more fragile and potentially unstable.

Fear and change breeds hate. And for some people, they just revel in being bigoted jerks.

Because people are insecure about their own sexuality, gender identity, or gender expression.
Because people fear frickin' EVERYTHING.
Because people are close-minded and continue to believe however they were raised.

The first thing which identifies people when they come out of the womb is if they are a boy or a girl. To mess with that can freak some people out. It is playing with those boxes.