If your girlfriend is always hiding or turning the laptop when your next to her what would you think?

ok my girlfriend for 5 years now is always doing this when of twitter or social sites,I want to ask her for her twitter password cause of the insecurity with that but I wasn't sure if it was the right thing to do, But I went ahead and she was like "No way,Not at all ,that I need to trust her. What do I do? What do you all think?
If your girlfriend is always hiding or turning the laptop when your next to her what would you think?
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