How does that puller attach to the wheel?
It looks like it screws on to the hub in place of the hub-cap.
Did you remove all of the washers and cotter-pins?
The photo shows what seems to be a Black washer in the opening.
Should that come out so that all you see is the end of the axle?
You also may need to move the car forward an back a bit, like 3-feet, back and forth, to “break” the wheel a bit loose.
On the front wheels, you. may need to turn the steering wheel left and right to break the seal / jam.
I did that a few years ago and found that I needed to put the wheel-puller on the wheel, torque it hard with a BIG WRENCH (or 1/2-inch socket with a pipe on it to increase the torque) and let it sit, on the wheel – torqued, for a day or so.
Even then, the wheel / wheels did not want to come off easily (50-year-old dried axle grease).
When you are doing this, I assume that you have the car on jack-stands so that the wheel is off of the ground.
If you do as I suggested about leaving it for a day or two torqued, you should also re-torque it once or twice a day (if it is possible) to increase the torque.