I don't know what is worse: to show interest or the opposite. But in both cases I think there is a paradox .
In case of me taking the initiative, I would only do it to a girl I would know well, making sure she was a good person. But then there's the pressure of taking responsibility for the consequences of that action:
- considering a positive response, she would get some expectations and even if she knew me, she would probably expect a "shy" limited relationship, not a "social phobic" one. That would disappoint her and lead to a not so good "chemistry"...
- considering a negative response, that would be an uncomfortable situation and full of regret
The paradox: personally I wouldn't do it... since I've never had a girlfriend and I can only guess the advantages, I think there would be more to loose. I see sometimes people saying online that they've just finished a >5 year relationship and things like that... I think I wouldn't risk to hurt/disappoint someone after some time and I can't deal with the fact of opening my personal "details" do someone I'm not sure that will stay.
In case of being approached by a girl, I think would be worse... I would probably take evasive countermeasures and would think she was joking just to see my reaction or maybe taking part of a bet. I don't think I would react positively. A few years ago when I was a kid, I used to spent vacations at my cousin village and there were two girls (sisters) that used to show up and hang out where everyone used to play, like many others. One of them was quite shy too and there was some attraction between her sister and my cousin. I don't know if it was true, but that was a rumour that she liked me. One day one the other kids said to me that she asked if I would accept to date her, and I quickly said no... he was kind of a clown and I obviously didn't believe him. Besides, if it was not true, that would be embarrassing to me to say yes, specially to an idiot intermediary. Not that I would say yes anyway, because I didn't even know what to do and behave after that... I'm not saying I felt "love" for her, but she was nice looking and also a bit shy, not very "show off" style, I kind of like that.
After all I think it was not so bad, because it killed the tension and I didn't worry about it anymore, but I didn't felt good about being approached in such a way. Anyway, we were all kids, there's a lot of pressure and I don't date for sport, so I think I did the right thing.
Conclusion: I don't think I would react positively to a girl saying she likes me. I would probably enter a "internal panic" state and say something to get out of the situation. Also, I'm even more messed up now than when I was a kid...
The paradox: I don't even have female friends so the probability of a girl saying me that she likes/love me is quite null... and I had to reeeaaally know her very good before I even consider she was being sincere about it.
So, there you go... "Destined to be alone: the recipe". :
: