I've um'ed and ah'ed about contributing to this, but having just left my 9th answer, I'll pitch in.
The reason why I hesitate is that I don't consider myself to be a contributor to maths-SX, so in the strictest sense I can't answer this question. However, I'm a "conscientious objector" in that my non-participation is based on a deliberate choice rather than apathy, so perhaps my reasons for not participating will be of use to you.
I probably need to start by explaining that, since the first two paragraphs are apparently contradictory. I keep an eye on this place as I think that it is a great idea in principle. I do participate in two other SE sites (MathOverflow and TeX-SX) and I really like the model. But as yet, I haven't figured out exactly how to participate here and until I do that then I'm not going to do more than what I currently do. And that is to drop by every now and then to see if there is a question to which I happen to just know the answer. Certainly, I don't put any effort in to answering questions here beyond the effort of writing it out. On MO or TeX-SX then I will willingly take up a challenge and work at something, but here I won't. That's what I mean by "not participating".
My reasons for doing that are nothing to do with the atmosphere here on meta. I'm a veteran of MathOverflow's meta (indeed, I suggested it and was the first non-moderator to sign up) and have had many blazing arguments with many different users (including the guy who set up MO) so I'm not afraid of a bit of fire on meta. But I think that the atmosphere on meta is another symptom of what keeps me from joining in fully.
The truth is that I haven't worked out yet what this place is for. And I'm afraid that the answers given previously don't help me figure that out.
I am a professional mathematician. That means that I get paid for doing maths. Actually, I get paid 45% for doing maths, 45% for communicating it, and 10% for ... er ... for helping ensure that the university runs well. So when I do a mathematical activity, I have at the back of my mind "If my employer walked in right now, would I quickly change to a different tab in the browser, or not?". Now, I can justify lots of mathematical activities. MathOverflow is fairly easy, but this place is hard. It seems to fall between two things. Let me deal with them separately.
Teaching: This seems obvious. By answering questions here, I am helping people to learn. Except that the part of my job that is teaching is not "teaching anyone who wants to learn" (would that it were!) but "teaching the students at my university". There aren't that many students from my university here (are there any?) and if there were, it would be an incredibly inefficient way of teaching them. I would be wiser to invest my time in trying to reach the students right in front of me than those half the way around the world.
Problem Solving: There are no end of problems in mathematics, and whilst we only write up the ones where we think we have something new to say, I'm sure I'm not the only mathematician who doesn't really care if a problem has been solved before or not, the important thing is: can I solve it? But with so many, how does one choose which to solve? An easy way to choose is: someone else wants to know the answer. So this site seems perfect for that. Except that the level of the problems here are not the level that I particularly want to get my teeth in to. Basically, I already get my "problem solving" hit from MO. I don't get it here. Moreover, since there are so many problems out there that I could spend time on, it would be wiser of me to invest my time in trying to solve those that might help me with my actual research than just those I happened upon whilst reading some bizarre website.
I have a suspicion that this site is far more "Ask an expert" than any other of the SE network sites. I don't know enough about the data explorer to do this, but I'd like to compare the various sites on their "questioner" and "answerer" populations. A quick look at the top users shows that very few of them ask questions here. Certainly, I can't think of a single question that I could ask here (where I really wanted to know the answer). On MO and TeX-SX, I feel that I am both an asker and an answerer. Here I would be/am just an answerer. At the risk of seeming a bit cold-blooded, what's in it for me?
Now, I am an expert in some things. There are a couple of things about which I am one of the best people in the world to ask. But they don't come up that often here (they don't come up that often on MO either), and there are certainly plenty of experts already here in the wider area that I know about. So you don't need me here. My not participating doesn't hold Maths-SX back in any significant way.
So, in summary, why should I participate in an SE site?
- To learn. But as a mathematician, there are more efficient ways for me to learn.
- To help. But there are more immediate people who need my help.
Now, I realise that this all reads very cold and calculating. It has to be precisely because I am not very good at being cold and calculating when faced with a problem to be solved. If I jumped in here, I would be going crazy trying to answer questions left, right, and centre; sure that I had the right answer that was going to enlighten the questioner and open their eyes to the beauty of mathematics. On TeX-SX and MO I can be like that because I know that I will also gain: they are true exchanges. Here, I don't see the exchange.
As a last ditch attempt to dispel the calculating nature of this, let me add that second to proving a sneaky theorem is that moment when you see an explanation hit home with a student. To watch their face when it all becomes clear and, for a moment, they glimpse Mathematics with a capital Mathematics is a wonderful experience. To quote:
Rose: I can see everything. All that is, all that was, all that ever could be.
The Doctor: That's what I see. All the time. And doesn't it drive you mad?
When teaching, those are the moments that make it worthwhile. Show me how I can get that hit here, and I might just join in.