DIAGNOSIS It's on there snugly by design. There's a specific release mechanism you need to use; pulling straight out like an old thermostat will feel like you're breaking it.
FIX Put your fingers on the sides of the thermostat display. Don't pull yet. Look at the very top of the display, where it meets the wall plate. You'll feel a slight lip. Gently but firmly pull the *top* of the display outward, pivoting it away from the wall plate. The top will release first. Once the top is out about an inch, you can then pull the bottom out. It's a top-release, swing-out design. There are no tabs or buttons to press, just a careful pivot from the top.
IF THAT DIDN'T WORK If it's absolutely stuck, check if something (like dried paint, or the edge of the wall plate) is physically catching on the display's housing. Use a thin plastic card (like a credit card) to gently slide between the display and the wall plate at the top to break any seal or obstruction, then try the pivot motion again.
HEADS UP The wires are connected to the wall plate, not the display you're removing. Once the display is off, the wires are still live with 24V AC from your furnace. Be careful not to let the bare wire ends touch each other or the metal wall plate, as it can blow a fuse on your furnace control board.