Question: I received an invitation to attend a relatives son's bar mitzva. I don't want to attend because he didn't attend my son's bar mitzva. Is this permitted?
This is called revenge and is forbidden under the rubric of לא תקום. The gemara [יומא כג] says that revenge is only forbidden in money matters but the Rambam [דעות ז ז] and Sefer Hachinuch [מצוה רמא] neglect to cite this gemara [עיין מנ"ח אות א] and forbid revenge in all instances, so even in our case it would be forbidden. If the person is busy and that is why he doesn't attend it would be permitted. If it is a mixture of busy and revenge then it would seem that if being busy was enough of a reason for him not to go then it would be permitted. But if he needs both reasons to justify his absence then it would be forbidden.
עפ"י חשוקי חמד רג