Lime (or other deposits from the water) can build up around the inside of the valve body behind the O-ring (see arrows). It is seldom much but is enough that the O-ring is captured.
Do NOT use any tools to scrape the lime. Scratches on the inside surface of the valve body can cause permanent leaks.
option 1) Use needle nose pliers or forceps to grip one of the tabs on the stem end and attempt to pull the stem end out.
option 2) Use a screw driver to push the stem end as deep as it will go. Saturate a paper towel with white vinegar, or a commercially available product, and place it inside the valve body as near the O-ring as possible so the lime will be dissolved. Keep the towel wet and allow enough time for the lime to be dissolved.
option 3) Push a 7/16" tap far enough into the stem end that the threads on the tap grip the stem end. Pull out the tap with stem end attached.