Anthophobia: Fear of flowers
She loves me, she loves me not... Well, those with anthophobia don't need to pick any petals to know that they don't love flowers. Those with anthophobia will even avoid going outside altogether out of fear they might run into a flower.
A common origin of this fear is looking at a flower, and having a bee come out and sting you, resulting in a desire to stay away from flowers altogether. Flowers are also often at funerals, which are sad and painful times, and the association sparks fear and distress in many.
For those who have very intense allergies, the fear of flowers could be quite functional, as they want to stay away from that painful time of the year.
So, if you're looking for a Valentine's present for someone with anthophobia, probably stick with chocolates instead of flowers unless you want them to run out on you immediately.