This is an odd one, though certainly not as odd as anatadaephobia (fear of being watched by a duck) or something along those lines. Hemophobia is strange, because it isn't usually single. This means people with the fear of blood are usually afraid of something else, like needles or other various pointy things.
Now if you break it down, hemophobia becomes a perfectly reasonable condition. Most often when a person is first introduced to the sight of blood in childhood, it is their own. I suppose this can cause one to associate blood with pain...and it can kind of just get worse from there. This is when it is purely psychological, of course, which hemophobia usually isn't.
When a person is exposed to the sight of blood, the body's reaction is to generally have a small drop in blood pressure. This is instinctual. Because when blood pressure drops, one is less likely to bleed or clot as much if injured. If your blood pressure drops TOO much, you faint. Sooooo...since fainting is usually pretty inconvenient, it can at times be another cause for hemophobia.
Most phobias are treated by desensitization. Hemophobia is too, but...it's also treated in another very unique way. Training one's body to raise their blood pressure, either through tensing muscles or engaging in vigorous activity.
So now that you've read a little bit about hemophobia, here's a short video from a personal favorite show of mine, to ease you into...some kind of...pun using the word vein. I'm not always on my A game here, folks. Much less my B or O game either...