There is a vast set of differences between spotting personality traits and patterns and truly psycho-analyzing a person. So, to jump into the debate... (And since there are many people involved at this point, let me state that this is an overall opinion on the topic, not directed at any particular poster.)
There is a reason that people who psychoanalyze for a living train and go to school longer than most of us own a car or live in the same place. It is one thing to read people's internet posts or interact with them online and notice patterns and quite another to fully understand the underlying reasons for those patterns and personality traits.
Mairead gave us a list of three things involving psychoanalysis. The third is treatment. You can't just do the first two without the third and consider it "psychoanalysis". You don't get to pick and choose which parts you want to perform.
Redmage stated that it doesn't take much to recognize a paranoid shizophrenic. Well....yes it does. Paranoid schizophrenia mimics many other disorders and is rarely diagnosed quickly, and never lightly, even by trained professionals. Can you tell by reading posts that a person is PS and not, say....dissociative? Or suffering from a state of regression? Considering the fact that the same "treatment" or even "personal dealing/interaction" will have vastly different effects for just those three possibilities would make me extremely hesitant to comfortably decide what someone I hardly know is apparently suffering from. The potential for damage is too great.
And that's the real meat of the issue here. Not only is the unqualified psychoanalysis of someone over the internet, someone you don't know, irresponsible...it's potentially extremely dangerous. It's one thing to gather information and collate it into a perceived summation, to "get a rough idea of what the person is about"....and quite another to understand what's NOT being said. The reasons behind things. People will foten say certain things, act certain ways, but hold the motivations for that close to the chest. Let's say a person says "Thing X"....but you don't know why. You think you do. You've put a few things together and pretty assured that you know why. But without it being said, you really don't. Now, let's say Thing X was said because a person is momentarily angry. Or, let's say that Thing X was said because of a deep-seated issue regarding abuse. Or possibly that it's physical and due to a chemical imbalance. Now, you respond with Thing Y, nopt knowing that underlying reason. In the first instance, it will do little more than agitate. Not helpful, but not anything we don't see every single day online. In the second or possibly third cases, you could inadvertantly trigger that person into something you didn't expect. Something potentially dangerous.
Because you were not qualified to see the larger picture. I'll share a little something here. Past couple weeks, I've been dealing with some things, and talking with someone online who has training. It helped a bit, getting an outside perspective. However, at a certain point, this person told me that there was only so much that could be done this way, that he was not qualified to go any further, from a distance and without knowing me better and knowing more of the underlying causes. And I've known said individual for some time.
So, I'd have to say that, no....I don't believe that we can psychoanalyze someone we don't know, or even someone we do if we're not qualified. We can help, we can offer support....but to attempt to psychoanalyze a person without the proper training and qualifications is not only irresponsible, but potentially very dangerous to that individual and to yourself. It's like a car...let's say you don't know a hell of a lot about cars, but you can "figure things out" pretty well. Your friend comes to you and says his brakes aren't working, and there's a puddle of fluid under one of the wheels. So, you hop online and tell him to replace the brake line for that wheel and bleed the brakes. What you didn't know was that the bleeder itself was broken. He does what you tell him, drives his car and gets into an accident. Because you weren't qualified and trained to look for the other possible reasons. A rough analogy, yes...but valid.
Bottom line is, we're all capable of reading into one another to some extent, some more than others. But true psychoanalysis needs to be left to the professionals. It's easier than you'd ever imagine to be wrong and cause more damage than you're fixing. And if you're going to decide to take someone's analysis upon your shoulders, you better damn well be prepared to put responsibility for the possible consequences on those same shoulders when and if you're wrong or misinformed.
Sorry for the long post, but I feel very strongly about this topic.