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This girl seems to be very needy for male attention. I think that it should be a red flag to you if she is acting mad at your for respecting that she has a boyfriend and not wanting to make him jealous. And what do the two of you really have in common that would make you good platonic friends? Do you take any classes together? Do you have good friends in common? Do you have any of the same interests or hobbies?
For a platonic friendship to really work between a young man and a young woman, they need to have more than just having personalities that get along. Anyway, I suspect that this girl is a needy drama queen and that it's not worth it to try to be platonic friends with her. After all, what would the two of you do together as friends anyway? Go to a local pizza parlor and just hang out? Would she expect you to buy her a soda and a couple of slices?