According to Christians, everybody is a sinner, including themselves. But the way I understand it, in order to accept Jesus, you have to admit your sins and get right with G-d and if you can't admit to sinning, then you are a liar, which I think may be another sin.

Not sure about that one.
Anyway, if I tell you Jesus loves you, but you gotta stop your sinning ways and make an honest woman of your girlfriend and get right with G-d, so you can go to your earthly reward, that shouldn't really offend you. It's not casting stones. It's telling the truth. After all, as your friend, I love you and want you to go to heaven right?
But it would offend you because you aren't Christian. You would consider me being intolerate of your "living in sin" situation, intolerant of your religious beliefs and so on and get mad and huffy and say "well you did it" and I'd say yep.

I'm a tad

but I think you get the point.
Christians want you to admit your sins, accept G-d and Jesus as your personal savior, and then strive to be a better person by not commiting those same sins any more. It's not casting stones as you say, but an honest effort to attempt to get you thinking about your wicked ways and how to turn your life around.
I've never met a true believer who has not admitted to being a sinner.
See you have to listen to the Chrisitian message all the way through to get it. I think a lot of people hear "I want to share the Good news with you" and they automatically shut down or become instantly offended and outraged instead of listening.
That's the thing. Lots of arguments and disagreements would NEVER occur if humans actually listened instead of instantly reacting. :shrug: