I can tell you from experience (as a student), and also based on the information you provided about this student (i.e. them being argumentative etc.), that they're unlikely to take your rejection well. You have to consider that, even though you might think they'll be a "pain" to work with (and your feelings may be justified), this student , who could have selected any other advisor on this project, selected you. Speaking from experience, rejection from a professor you want to advise you hurts. A lot. As such, this student is very likely to escalate the situation, perhaps even complain to administration, especially if you reject them but they find out that you subsequently accepted other students.
I like Arthur Hv's idea of devising an objective guideline as to how you select students. This way, all students have an equal chance of working with you, and if they don't objectively meet the criteria, they have no cause to complain.
I disagree with baldPrussian's advice. While you are not obligated to provide the student with any explanation, this can further escalate the situation. For example, in my case, I regretted writing to the dept. chair when my professor declined to assist me, and I didn't like the way he handled the situation. (Very long story.) Like baldPrussian is suggesting, administration tried evading my questions, not providing answers or explanations etc., and I complained all the way to the Board of Regents (not about the prof. but about how the chair/admin. mishandled everything) and filed a complaint with the attorney general's office which I'm still waiting to hear from.( Now that I believe I have a chance of being accepted to another university for grad. school, I'm not as hellbent on pursuing this; I'm undecided right now.)
Anyway, my point in sharing that was to show how a relatively minor situation can easily escalate. My suggestion is to try working with this student. Even though he or she may not be your favorite, you should see it as part of your job, for which you're being paid extra. However, you could also give them a clear set of expectations, and if things don't work out, you can always discontinue working with them.(If they complain, you'll be able to provide evidence as to why you did so.)
Alternatively, if you feel that strongly about not working with this student, you could (if applicable) tell them that their project doesn't fit well into your area of expertise, but suggest another faculty member whose research area correlates better with the project. This way, they don't feel as rejected or like you don't think they're competent/intelligent enough etc.
Again, I'm not saying that you're wrong for not wanting to work with this student, but they can jump to all kinds of conclusions which can fuel a myriad of negative emotions and reactions. In some sense, they may be correct, as you really don't like them, though they might not realize that it was their arguing etc. and instead take it as a slight.