i have old (late 1980's) recessed lighting. i cannot figure out how to remove the can. there are no springs,ears or anything i can see inside the can. the bulb holder is secured by 2 spring clips that fit into slots at the top of the can. the cover is white plastic that fits into notches in the can and screws to lock in place. i have removed the plastic cover and removed the bulb holder and felt around the top of the can for any type of release pin. it appears that the can is pushed into the ceiling and then spring clip secure it to the drywall.
Chances are that this fixture was installed at the time of the home's construction. It'll likely have two crossbars that were installed across the gap between the two adjacent roof trusses or floor joists:
Removing it would require access above the ceiling, or you can attempt to cut and disassemble the unit through the hole in the ceiling. If you can release any tabs that secure the can itself to the base plate you may be able to push the can up out of the way, allowing access to the crossbars.
Be aware that there's likely blown or batt insulation above and around the can. Take precautions to not get it in your eyes or any other sensitive or delicate places.
Can you see what brand it is?
What you describe sounds very similar to what I had in my ceiling. It was an older Lightolier model.
My Lightolier can was shaped more like a rounded cone, rather than a cylinder. At the top of the "cone" was the electrical connection and bulb threads, which you could pop out by pressing on two spring clips. I couldn't figure out how to remove the can either, but my electrician managed. My guess is he twisted it about or released some of the clips somehow. But he managed to remove it pretty easily.
At any rate, if you can get the brand and model, maybe instructions are available online.