Over-qualified candidate for a master programme? Yesterday I had an interview with a professor. She was trying to show me that I am a over-qualified candidate for the master program... I asked her would it affect my chance? She told me she wouldn’t definitely introduce her ‘personal opinion’ in this decision and she emphasized that will be my decision... After the interview, I think I couldn’t convince her why I applied to the master program (I couldn’t apply for the Ph.D. program this year at that school).

However, I’m too worried... I haven’t yet received any email regarding my application... Should I send a followup email to her telling what my reasons are for applying to the master? Is a ‘over-qualified’ candidate meaningful in a master program in natural sciences like physics, chemistry and etc.?

Should I send a follow-up email to her explaining my reasons after the interview? I really don't wanna lose this position...
I doubt that a follow up would be needed. I interpret her reluctance to tell you her decision at the time as just an ethical requirement. She would, I hope, say the same if you were under qualified. 

You might want to send that follow up if you didn't discuss the reasons in the interview. But make that note mostly a note of thanks for her consideration. That would be a very natural thing to send.