My girlfriend too naive to realize other guys flirting?

I have been dating my current girlfriend for only 3 weeks and I'm already finding a little suspicious/uneasiness. I've met one of my girlfriend's friend (a guy) for the first time and id told him I'm the boyfriend. While the three of us had lunch, just from the observation, id had a uneasy feeling about this guy because of signs such as when he talks, he looks directly at her instead of switching back and forth. After Id left, for the past three days, he has been constantly showed signs to always make plans with her because he needs "relationship advice"...staying in the library with my girlfriend for the whole night. The last sign is that he told my girlfriend that he does not want to see me again, thus if he and I happen to make plans on the same day, my girlfriend would have to choose who to hang out with. My girlfriend is the type of person who goes out of her way not to disappoint other people and I am not sure if either she is naive that he is clearly using his "unstable relationship problems" to lure her or if I'm overestimating the situation. I want her to have her own time for friends and I don't want to lecture and control her decisions but I feel that every time she hangs out with him, I am letting the guy friend to flirt/ make his move.
My girlfriend too naive to realize other guys flirting?
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