Calling our fear a phobia is more than an attempt to dignify our anxieties with a grander vocabulary--although, of course, it is that too. But more to the point it is an attempt, in howsoever small a way, to distance our fear from ourselves, to eject it into the discourse of medical science rather than face the unsettling truth that fear is the core primary experience of living as a human. A coping strategy, in other words.
But it involves a significant conceptual slippage; something to do, I think, with the suffixability of the term. Like the -holic in, say, rageaholic which permits us to separate out or core, constitutive anger as an illness dependent (as alcoholism is upon alcohol) upon an external quantity, so describing oneself or others as 'phobic' deindividualises the experience of fear at the same time as it limits and shrinks it. There is, after all, a difference between 'fear' and 'a phobia'.
One function of this is the semantic shift whereby angst becomes a morally reprehensible social quality, and subject to the processes of social outrage. Thus rather than thinking of a homophobe as somebody made anxious by homosexuality (which he may very well be) we think of him as motivated not by fear at all but by malign hatred and bigotry. (An equivalent: not 'I have a profound fear of heights, or of open spaces', but 'I am motivated by a socially deplorable and evil attachment to the ground, or to enclosure'). This, presumably, cannot be disconnected with the fact that angst itself is, or is commonly thought of as being, much more widespread in Western cultures now than it has ever been before. Using the vocabulary of fear to describe the phenomena of hate reflects, in part, upon our own anxiety about anxiety, our self-hatred.