What is going on in this situation?

we dated for two yrs. i broke up w/him for good reasons. i kno he loved me but we fought a lot an we tried to make it work so hard. stress built up between us an it destroyed us. two days after we brk up hes holdin hands w/another girl an walkin her to class. . he says for me to move on and he will never be w/me again an but that he still cares about me. but he WILL NOT admit to bein w/her. . . if we are as done as he says we are, why does he think lyin will make a difference? why does he still like after were "done for good"?