Electrical – Light fixture mounting bracket too small to attach to junction box

A sawzall should make quick work of this. If you don't have one and know no one that does, they can be rented. There are also handles that clamp onto hacksaw blades so you sort of have a small, manual sawzall. It will take some work, but you will be able to cut enough that the remainder can be twisted off or chiseled aside.

If done carefully and methodically, a dremel tool can do much of the work without starting a fire. Try to direct the cut so that the sparks are ejected mostly downwards. Stop often and check the area for signs of burning. Have a spray bottle handy to quench any embers, as well as a fire extinguisher just to be safe. When finished cutting, spritz the area with water and check the area frequently for the next hour for any signs of embers developing.

Finally, depending on the finish, cutting and patching the ceiling is not that big a deal, then you can ensure the new box is properly supported instead of relying on the little tabs of the old work box and ceiling material for support.

If your box is that small it is almost certain that it is not a fan rated box. If it is not, then the box MUST be replaced with a fan rated box.

Sorry, but even with approval, someone unlicensed, uninsured, and unqualified SHOULD NOT be doing electrical work in a place that they rent. This is a perfect example; something as "simple" as changing a ceiling fan turns into a project since the box has to be replaced, and in an older house this can be met with issues.