Some years ago (you may remember those days as "back when Bubble couldn't stop posting about how crappy his love life is"
), after I broke up with my then-girlfriend, I sort of went through the same (by which I do not mean to imply anything more than "similar situation"). With my gf out of the picture, I found most of my interests were solitary (reading, playing computer games) and, with most of my social life having been frat stuff up to that point, I was...well, not lonely, but definitely alone a lot.
And while, as QP said, it can be hard to open up about yourself, it's still, relatively speaking, easier to speak about relatively safe things about yourself ("my day was X", "my job Y",...) than it is to actually be interested in someone else.
Frankly, most conversation about people falls into a few categories. Useless small talk (yeah, so it
is hot today. I know, why talk about it?). "Safe" but boring conversations (Those Nicks sure showed them All-Stars, huh?) that aren't, in point of fact, interesting at all, unless they happen to be about a sport/hobby you're interested in. People talking about your problems, people talking about their problems.
Talking about your problems - no fun and not what you want to do with someone you don't know well.
Talking about their problems - safer but less interesting unless you're actually emotionally invested in that other person - and
that is scary as fuck, and/or hard.
Obviously I don't know what the reason(s) may be why you find yourself talking more about yourself than about the other - but I've found that part of the reason, for me, is that I simply can't bring up the energy to actually
care. Not in the "my problems are so much worse than yours" way, but...I dunno? I can't really describe it properly. There are 7 billion people in the world, and I'm pretty sure about 5 billion of them are miserable (the rest is nuts or lucky or both). I can't care about all of them. People I'm already close with, I care about. People I'm not already close with....it's very hard (well, I've gotten better at it, but still) to make the effort to be interested in them, to open up and really listen, feel with them, try to be supportive, and so on. Much easier to just keep the talk either polite but general or to talk about "safe" subjects about yourself.
Not that I have any sensible advice to give based on that. Sorry. But hope you manage to gather up the energy to do something about it - I know that's what I still struggle with most.