Trying to figure out how the button you push in isn't able to push out the lug connector's nub far enough to let the lug slip out.
Skip down to 2.2 (particularly Fig 2-1) here:
https://developer.apple.com/watch/bands/Band-Design-Guidelines-for-Apple-Watch.pdf
Nice diagram.
This has happened to me too. Fake link band off Amazon: Looked ok but construction was trash. The lug's latch aparrently fell apart while inside the watch and the little pieces jammed up the sliding mechanism. I freed it by wiggling back and forth while randomly pressing the release button on the body of the watch. I was lucky.
To explain: The latch in the lug (part # 4 in your diagram) is made up of a number of tiny parts. At least three, possibly more: (1) The rubber bit on the top of the band, (2) the
hollow metal latch on the bottom of the band and (3) a microscopic spring that sits
inside the hollow latch piece and pushes it away from the upper rubber piece. There may be more parts, but it was too small for me to see clearly.
OP: If you still can't free it by wiggling with soap (or maybe some wd40??) you could always try a metal cutting wheel in a dremel. It will need a really steady hand, but you may be able to cut a longitudinal slot in the middle of the lug and slice through the jammed up latch mechanism parts in the middle? That's really a last resort, of course. Like if you're over it and ready to throw the watch in the trash.