Usually you slip a flat screwdriver in slot 3 and flex the screwdriver from a horizontal to vertical position and that will release the clip. Once all four are released they should pull out.

Looks to me like running an exacto knife around the edge to cut any paint between the can and the ceiling might be in order.

"Release the clip" may be a bit unclear. The visible portion of the "arm" as you call it needs to be slid downward. That will allow the arm to rotate from outside the can -- where it presses on the ceiling -- into the can. Once all the arms are inside the can, you'll hopefully be able to remove the can from the ceiling.

@Sigrid I agree.

@wdccruise Thank you for the helpful diagram.

@HALLETT & Co. I tried pulling down on slot 3 with a flat screwdriver (attached a new photo), but I'm not sure how to apply leverage other than having the screwdriver rest against the ceiling as I push upwards on its tail end. I applied quite a bit of pressure against my ceiling (trying not to break it), but no luck getting things to budge. Perhaps I'm doing this wrong?

Take a quick look at this video which shows how the clip (aka "arm") is slid into the slot in the side of the housing and then pushed up to lock it in place. So I think you want to slide it down it down slightly so you can swing the clip inward and then remove it.

But why are you removing the housing? Are you planning to replace it with something or just drywall the hole?

@ wdccruise Thank you, I was trying to find such a video, but I didn't know how to search for "clips". I think my first challenge is even getting the clip to slide down a bit in the first place, but I will try again tomorrow. The other question is what tool to use pull the clip and swing it inwards.

I'm removing the housing to replace with canless recessed lights.

@ wdccruise Thank you for pointing that out.