Cognitive dissonance on a personal level. On greater levels, we threaten to disturb established order and human beings often don't like change, on the whole.
Ideology - like a religious one in which you are taught any deviation from the norm regards sexuality or presentation is some affront to god. Obviously believers are going to struggle to some extent with the cognitive dissonance of that when presented with us.
Upbringing - a force of habit. If your parents tried to beat it out of you or you wanted to please them by doing what they say and they say trans folks are bad...
Community - you might be surrounded by people who really don't like trans people. To go against the grain and step out of line in some communities is to come in for flak yourself.
Biology - I know from my own experience how "weird" being trans can feel. There's no denying that it can feel weird and wrong. Like something just isn't right and is off-kilter. It can cause severe emotional distress in us. And I think that's why it causes it in others as well... there's something about us that, while I believe we are natural phenomena, is off-kilter to the norm. People know this as much as we know it. The average person is not given to exploration and open-mindedness unless confronted with stuff that forces them to consider it. I think biology might be the greatest source of that cognitive dissonance. Our species is very dimorphic, sexually. As such it's primed to lock on to the differences between the sexes and sort people into categories. When they don't fit easily into categories, the human brain is either intrigued.... or repelled.
Sexuality - it's a delicate area. Not unknown for the most homophobic or transphobic people to eventually be exposed as secretly attracted to the same sex or to trans people. Without getting too heavy into psychology bumpf, there is something known as "disgust sensitivity" in the field of psychology that people exhibit. Some have more of it than others, but it's thought to be a means of how human beings and human societies (as well as animal societies) regulate behavior, and how morality is mediated. Notice how sexuality is often tightly bound up with ideas of morality in most human societies? and people often have a very strong response to the topic of sexuality that often goes immediately to whether or not they find it "disgusting?" and how if asked on a topic relating to sexuality (or transsexuality) some people will be fine with it and others respond with something like "that's disgusting?" That's because their sense of morality is closely tied in with disgust sensitivity. It's been found that people who are more conservative in outlook and political orientation are more likely to be easily disgusted. Their disgust sensitivity to things outside the norm is higher than that of more liberal-minded people, and the blurring of lines or crossing of those boundaries tends to illicit a response/emotion of disgust in them. Disgust does serve an important biological function - e.g. most people instinctively find human waste or a dead body disgusting, and it transmits disease so there's a good reason to stay away from it. But we also end up judging and processing lot of other social ideas through the idea of disgust, especially things that challenge us morally or biologically. Unfortunately, being trans does challenge other peoples' biological/sexual perception of us, as well as many moral ideas in society, and so we are sometimes met with "disgust" as a knee-jerk response. It's not just social though. It's not something society could be fully accustomed to and trained out of, when you consider that straight men or straight women also often have a disgust response to the idea of sexual contact with the same sex. This often seems to just be a visceral response, not necessarily coming from a place of malice... and so if they should discover a person they are attracted to happens to be a trans person, there is always that potential for a feeling of repulsion and/or disgust as an emotional response in such a person.
If you want to get into the guts of why societies so often have a problem with gay and trans people, that can branch heavily into evolutionary psychology, biology and psychology, which I find fairly plausible in most respects as to why people might have this reaction. While "hate" can certainly be a bi-product, hate itself doesn't come from thin air, and there is no biological reason to hate something for nothing. We hate what we see as a threat, usually. Or what we've been conditioned to see as one. It's clear at this point that many people see us as a threat because as a demographic we appear to be growing. As a demographic many people have joined us, whether they fit the medical definitions of being transsexual or not. As a demographic we now ended up on the cutting edge of the "culture war", as they call it, whether we wanted to be there or not, and we have been politicized. The latter example is indeed a credible threat to conservative values, if you consider how certain trans activists now advocate eliminating the idea of gender altogether, or of adding many more genders to the lexicon, or of scratching the biological/scientific definitions of sex, or of asking drag queens to read to schoolkids. Whichever way you look at these things, they are a challenge to the established order and as such will be viewed by some sections of society as a dire threat to all they know.
Politics - we were less politicized in the past and certainly seen as less of a threat than we appear to be now. If transphobia is on the rise, I am not surprised, given that we have stopped being quite so passive as a group and trans activists now managed to gain the upper hand in some circles. Difficult situations like the desire to teach young children about LGBT in state schools haven't escaped the notice of many people and some see this as a deliberate attempt to indoctrinate kids. Once we moved from the arena of fighting for our rights to this sort of thing, we effectively shifted from being seen as a persecuted group to one who seeks to impose itself on the rest of society. This has intensified transphobia among the more conservative-minded.
