The easiest way to understand homophobia is to believe that homophobic people are lashing out against feelings they have themselves and can't or won't face, that their sexuality is insecure and they are in reality warring against themselves as much as anyone else. That explanation, however, is false, and believing that it's true makes us just as guilty of "phobia" as they are.
With a very small percentage of exceptions, homophobic people are completely secure in their identities, they do not have any latent homosexual tendencies, they are not trying to pull the wool over anyone's eyes. They are, however, quite limited in their ability to be objective on human sexuality because they lack the knowledge and experience necessary to finally realize that they are not being threatened.
BenderBoy said it best: people tend to hate (or more specifically, fear) what they don't understand. Call it a remnant of our evolution from the animal kingdom if you will but it's the truth, and each and every one of us has been guilty of the same thing when considering some facet of human diversity.
Our innate default response to something unfamiliar is to move away from it, as a means of precautionary self-preservation. Animals in the wild, when confronted with something unfamiliar, will generally move a safe distance away and then stop and stare, sometimes for great lengths of time, until they can determine if the unfamiliar is a threat.
If people could determine for themselves "does this really affect me, does this truly threaten me in any way?" things would be much better. Unfortunately, most homophobic people don't know enough about it, or have heard so much conflicting information, that they simply can't answer those questions. In order to find out for sure, they would have to do research, talk to and get to know some gay people, walk a mile in their shoes, etc. In short, they would have to educate themselves...and very few are willing to invest the time to do that.
But things are improving around the world, and one of the main reasons is that people are now being educated whether they want to or not. We have more forms of media than ever before, and the myriad variations of human sexuality have permeated those forms to the greatest degree in history, and it's only going to get more pervasive as time goes by. People who would say "I don't want to even think about it" no longer have a choice.
It's not insecurity that fuels homophobia, it's ignorance. And that's a good thing, because ignorance can be cured. It's happening little by little every day.