Is it normal that people like me more than I like them?

self–absorbed
adjective self–ab·sorbed \-əb-ˈsȯrbd, -ˈzȯrbd\

: only caring about and interested in yourself

I'd like to objectively disagree with you because:

1) I genuinely care about them. But it doesn't mean I like them. I like to care about them genuinely because it is the right thing to do, yet I do not get attached to them

2)I don't like being a nuisance to others with my problems, that's why I don't like to share things about myself early on, and so I am interested in their welfare

3) I make sure that I do not owe someone something/repay what I owe them in terms of favors and other things, so I am considerate in terms of reciprocity

So no, I am not self absorbed.