Is it normal that i get offended by people who defend their personal space?

I want to start off by recognizing that everybody has a right to their own personal space. That being said, I must say that I feel quite awkward about the fact that when someone goes to great lengths to exclude me from theirs, I become deeply offended. I'm no "close talker" and I'm not an annoying or irritating person by nature. I'm quite reserved and polite actually. I'm not exactly complaining here of getting my direct spoken advances rebuffed. It's actually more the negative "vibe" that some people give off that offends me. I'd better give an example:

Say, you're on a train and you see somebody interesting across from you who's reading a book you really like. Maybe they look look sort of lonely and appear to want to talk to someone. Perhaps they keep losing interest in their literary distraction, or they're sighing a lot and looking around hopefully. So, naturally, you see an opportunity, and you might just look up and smile at them, not eagerly, just politely, but instead of smiling back, they look incredibly uncomfortable and turn away. Even worse, they might even look angry or affronted by your kind gesture. You come away feeling as if you must be some kind of disgusting or unappealing human being, but even worse than that, you realize that maybe making a new friend as an adult is next to impossible, even with a shared interest. I know a lot of this is irrational, and that's my point. Even though I know I'm taking this kind of thing too personally, it still bothers me to this day.

Now, I should say that I am indeed a lonely and probably somewhat needy person. But on the flip side, when someone takes the time to talk to me or notice me, I'm extremely flattered and almost honoured by it. I appreciate small kindnesses and try to give them out as much as I can. Even I don't like overly instrusive or eager strangers, but why must we close ourselves off to the world? Why can't we make temporary friends on the bus? Wouldn't that make life so much more wonderful? If you're travelling with a friend and you notice a peer travelling alone, wouldn't it be awesome if you could include that person too? Let them in on the jokes? This kind of thing is normal in childhood, but it's almost frowned upon in adulthood, and it makes me terribly sad to see all these lonely people everywhere, unengaged from the plethora of possible friends around them.

Part of this way of thinking on my part, I believe, is due to that fact that I didn't grow up in a city or town, so I wasn't used to seeing people everywhere. In the country, it's almost code to be friendly to everyone you see. In the city, most people look down at the ground or at their phone/tablet and try to avoid eye contact with one another. People almost seem grossed out by strangers; by fellow man! We choose to live in a place teeming with people, but we live as if we exist in solitude.

Is my thinking at all normal? Would you be accepting if someone approached you wanting to be friends? Do you, yourself, make the effort with others even if it usually fails? Thanks for your responses.