Is introversion unfair to other people?

I am an introvert but I also make friends easily and one of the biggest problems I've found is when people want to talk more and more and i just want to retreat. I'm torn between wanting to be a good friend and just wanting to escape. It's even worse because I'm the one who offers to be there for them, to listen to them, because I do care, but then I can't do it, it's so overwhelming. HELP. I feel it's very unfair to them to make it seem like I'm dependable when I'm really not. Should I stop trying to reach out to people and just embrace my introversion/loner tendencies, or should I try to overcome this periodic need to withdraw? And if the latter, how should I go about it? Thanks for reading and responding if you do!