It'd risk rubbing Damian the wrong way, seeing as how Damian is all "my dad, not yours, mine mine mine". Damian doesn't want to acknowledge the bond between Bruce and Dick as being as legitimate if not more than his relation to Bruce. By playing into it, Dick makes sure that Damian focuses on the important thing - le Bossu = bad guy, it's personal - instead of taking the chance that Damian would bicker or rebel later on.
Dick also says that le Bossu went after him, as a part of what makes it personal. By wording it that way, he makes the link between Damian and him and leaves Bruce out of it.