First, universities always treat faculty differently. You're just a student researcher. Don't expect faculty rights. It's crappy that's the way the world works, but it does.

Most places consider software written while being paid for by them labor for hire. As such, they own what you create. In this case, the intellectual property rights to the software. This isn't that different from a construction worker building a building - he doesn't get to take what he made when he leaves. The difference is that software is infinitely reproducible in a way that doesn't harm the original.

Still, this is par for the course. Work for Google, Google owns the code you write and you can't take it with you when you leave. Work for Microsoft, MS owns the code you make and you can't take it with you when you leave. Work in this position, the University will own the code you write and you can't take it with you when you leave.

You might be able to negotiate something nice - Universities are non-profits and if you argue for an open-source license they might be genuinely receptive. If you want to push, think of it from the University's standpoint: does it help the school (to give you the code)? does it promote the school's mission (to give you the code)? does it promote the school (to give you the code)? That's unlikely, but under a FOSS license it might promote academic research and the school might like the openness of it and the possible free promotion they'd get if it caught on.