I'm going to go ahead and say that some people do want others to assume more of the risk. I'm kind of one of them, but I've been stepping out of my comfort zone over the past few years so that I can take care of my share of the responsibility for socialization. I have noticed that, overall, I tend to wait to gauge the overall atmosphere of a situation before I chime in. Once that's done, I have no problem 'steering' things in some given direction when needed.
It seems that a given level of socialization and personal discussion is "less risky" for some and "more risky" for others. Some people seem to give off the vibe that socialization isn't a huge risk for them--that they're content to just chat it up with many people, sharing a plethora of information about themselves without batting an eye. To an extent, that's pretty commendable.
Some people are just much more comfortable taking the initiative in that respect than others are. Some of the underlying factors could include anxiety or not wanting to offend others. There are more positive motivations for that mindset out there, though.
I think that, sometimes, it's a matter of incremental, small risks. You share just a little bit, then I reciprocate, then you know that you can trust me a bit and share a bit more, and so on and so forth until we get to know each other.
I understand how difficult that 'initial push' can be--not that it's an insurmountable challenge, by any means. But some have an easier time with it than others do. Moreover, if I don't reciprocate, then you'll feel at least slightly cheated. So I suppose, at that point, you'll have a choice--either continue, or don't. Both of those choices are understandable. If someone gets 'burned' too often along those lines by putting it all out there, then perhaps not sharing everything all at once is the key.
There are reasons to not put it all out there or to reciprocate when another person does. If the context is 'off' (e.g. at a 'cliquish' workplace), then, well, sometimes it's best to truncate the depth of a particular conversation at some acceptable level.