What are the possible reasons for missing 3 periods and not pregnant?

Well it could mean four things.

1. You are going through menopause (the point in a woman's life when she stops her periods)

2. You are pregnant and you have taken a faulty pregnancy test

3. You are irregular (when a girl does not have her period once a month, she doesn't know when she is going to have it)

4. There is something seriously wrong with you.

In all four of them cases I sincerely urge you to see your doctor because it could be serious.