My cat is like this. He does not like to be picked up and placed on
anyone's lap--he likes to decide when he wants to be there. He will sit
on my lap on the sofa, now that he is older, but never when *I* want
him to, only when he feels like it and he leaves when he is "finished
with me."

When I'm focusing on something else (the computer, the t.v., reading a
book) he gets jealous of not being my center of attention and suddenly
he wants attention. I also think it is a cat thing (for some cats) that
they like attention, but not too much of it. I think that's the same
reason they'll seek out the person in the room that wants them to be
there the least. That person is not staring at them, which makes them
feel more comfortable.

Your cat may mellow as she gets older too. I was sad that after my cat
grew out of kittenhood that he wouldn't be a "lap cat" anymore. But now
that he is older, he has grown to like it (but even now, he sets the
length of time he is there. He likes to feel in control!)