I bought a new 2008 Impala LTZ which had a very similar ceiling mount fixture (other than it had a built-in eyeglass holder also). When delivered, the eyeglass holder was defective and the dealer ordered a new part (whole assembly - not just the eyeglass holder).
The dealer replaced the part under warranty and inadvertently left the old part on the RF seat. Before I left, I returned it to the service advisor. I looked at the part before I gave it to him.
The rear of the assembly had a variety of metal spring-type push in clamps that snapped into holes in the headliner / ceiling. There were no screws or permanent fasteners. I was sure it simply pulled out of the ceiling, and the wiring connectors removed to be transferred to the new assembly.
If you have tried to pull the fixture down, it may just have strong spring-clamps, which are difficult to remove (and make you feel as though you will break something). Perhaps you could get your fingers from both hands under the edge closest to the windshield and pull firmly?
A picture is worth a thousand words (although the lack of one wouldn't keep me from trying to explain a thing in less then a thousand).