I would say neither. Fear often gets lumped in during most debates with several other human tendencies(such as sexuality, for instance) in a black and white spectrum of either "it's a choice" or "it's an inherent human trait and nothing can be done about it." Like sexuality, I don't believe it's simply one or the other. People don't choose to fear things; but at the same time, there's a lot people can do to change what it is they fear or get rid of it completely.
For example, I know someone who is deathly afraid of bugs. I don't believe she ever got out of bed one morning and thought, "Gee, from now on, I'd really like to be terrified of anything with six legs." And yet she is, nonetheless, mostly due to the way her brain functions. She never made a choice to be like that. However, if she really wanted to put the effort into it, I'm sure she could conquer said fear. Either by forcing herself to get up close and personal with them, or, if necessary, through therapy. Not that necessarily either one of those would be worth getting over the fear...but she still technically has a "choice" to overcome it.
So in the end, I don't believe the idea of fear fits into the black and white spectrum of either "completely a choice" or "completely not a choice." It's in that grey area inbetween.
