DIAGNOSIS You're not doing it wrong; the lid is designed with a very tight, interference fit to prevent leaks under high pressure. It can feel stubborn, especially when new or if the container rim has a little residue on it.
FIX There's a specific technique. To put it on: align the lid's pour spout with the handle of the container. Press down firmly with the heels of both hands on opposite sides of the lid—not the center plug. You should hear and feel a distinct "click" or "pop" as it seats. To remove it: grip the container handle with one hand, and use the heel of your other hand to give the front edge of the lid (near the spout) a sharp, upward *tap*. Don't try to pry it up evenly all around.
IF THAT DIDN'T WORK Check for debris. A tiny grain of rice or a bit of dried smoothie on the container's sealing rim or the lid's rubber gasket will prevent a proper seal and make it seem stuck. Clean both surfaces meticulously with a damp cloth.
HEADS UP Never run the blender without the lid fully seated and locked with that "click." At high speeds, the contents will absolutely erupt out of the top. The tamper is only to be used through the center hole in the lid when dealing with thick mixtures.