I think they are lonely.
Yes, very much so. Because think of the abusive behavior people who behave in such a way were subjected to by their parents the entire time they were growing up in order for them to think that their - to us - unusual behavior is 'normal'. People generally behave the way they were treated... if they are extremely socially awkward and don't have a clue what acceptable behavior is, it is because their parents had no clue what was acceptable (or did 'unacceptable' things to them).
People aren't generally what many would consider inappropriate assholes by choice. They learned the best they could how to behave from people who likely at best treated them as a burden, but more often as an emotional punching bag. And, unfortunately, every time someone is extreme in their response to a person who grew up that way, that person is actually reinforced that that is - indeed - the way people act toward each other. And they become further and further withdrawn and confused (or more and more inappropriate or angry).
So yes: lonely. Trying desperately to connect (because they likely never really have connected with anyone since birth), but having no social skills with which to do so. The reaching out with, "we're going to be friends," is the awkward attempt by someone without social skills to try to connect with others. To most of us (myself included, had I received one of those PMs) that feels kinda' creepy and the tendency is to avoid the person. For someone to make contacts like that, though, says to me is that one or both of their parents were grossly invasive.
Sad, really.
Edit: Does this mean I think these people should be coddled or that I want to associate with them? No (I'm no longer being paid to do treatment, now I can choose what I share and with whom). It means that responses that are basically neutral in tone, but explaining what isn't acceptable are most likely to help and get the desired results. When a couple people here tried this, and the person escalated things further, banning seemed to me the appropriate response as it was clear the person was too far gone to comprehend what was being said and why [if anyone cared what my personal opinion was on the specific events of the last 12 hours or so... likely not, I'd gather].
Likely more than enough fuckin' psychology for now. If I wasn't so far past capacity I wouldn't have written anything to begin with on this [and, likely, many would've been happier for the lack of it being here because they didn't sign up for a Developmental Psych course]. So: enough.