Any "__phobia" is, naturally, always about fear.
Does it really matter to Bob and Ethyl in Buloxi, Mississippi if two men in Oregon want to settle down together? Of course not. It's irrelevant to their lives. But it's true that gays exist. They just don't want to see them in their neighborhood, because people who are different make them uncomfortable: Muslims, blacks, Jews, gays, Democrats, what have you. They fear their differences. And in some circumstances, with gays, they fear that knowledge or visibility will turn their family members gay.
When you don't allow gay marriage, and when you support a "don't ask, don't tell" policy in the military, that gives those uncomfortable, and fearful, of those differences the safety zone of denial. Denial is a convenient tool when they encounter gay men in Buloxi, MS -- because they are most certainly there. It's an extra measure to play pretend that homosexuality doesn't exist, and with it they feel a little more safe from it.
The same motivations power a lot of the people who object to things like access to birth control in high schools. Everyone knows there are kids are having sex -- whether or not their school makes birth control available or not. And religious dogma aside, there's little argument that access to birth control for sexually active people is a better social evil than no access at all. But by preventing access, parents can take the psychologically safer (though practically less safe) route of continuing to deny the fact that their teenage sons and daughters are actually having sex.
That veneer of denial is very important to a lot of people. Many people like to live their lives with their heads buried in the sand, so you best not try to take their sand away. They could get ugly.