I am not sure with what you are showing here why it is not working since i can not see the remove_me() function but I will show you how to do it the way i would do it.
you could use $(this) in the remove_me() function like so:
$(this).closest('li').remove();
This would start where clicked and go to the closest li tag and remove it.
(darnit two people just answered ... im not going to look ... got to learn to type faster lol)
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…