Well, it looks like you got the strainer out, but the strainer wasn't designed for the drain. It appears to have been caulked in place on a leaded flange and the floor is concrete. BTW, thanks for the photos, they really help. If I understand you correctly, you are pulling up on the vertical part of the drain. It appears to be a cast iron tailpiece, straight down to the p-trap.
If so, the tailpiece can't be removed unless you break up concrete and repipe the drain and trap. I guess it would be better, also, to describe what end-result you want. Do you want to skim-coat with concrete and retile? Remove all concrete and start from scratch? Just replace the flange and drain? Just some examples on info that could help some of our guys get some insight.