Someone who has a crush on a fictional character makes up 'their' version of that character in their mind and they govern how that character interacts with them. I also agree with naturalplastics that if the character was a real person, and there's only one of them, they'd have their own wants, needs, standards and I'd add - if they have partner appeal to a lot of people they'd be quite high-demand and out of most people's reach in terms of social status.
This is a bit like how every Christian has their own 'Jesus', ie. it's the biblical and cultural figure mixed with private spiritual leader, teacher, deity, etc.. The application of the concept is just different in this case because most people have a spiritual rather than sexual relationship with Jesus, whereas with a fictional character they have a crush on it might be less context-restrictive.
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“Love takes off the masks that we fear we cannot live without and know we cannot live within. I use the word "love" here not merely in the personal sense but as a state of being, or a state of grace - not in the infantile American sense of being made happy but in the tough and universal sense of quest and daring and growth.” - James Baldwin