Can philosophy be debated? In a loose sense, yes, but not in a strict sense. I say that if debate is occurring in a certain place, then no philosophy is occurring in that place. Philosophy is not a matter of debate. That is a nonnegotiable point with me. So I won't debate it, nor can I consistently with what I have just said. It is after all a (meta)philosophical point: if philosophy cannot be debated then the same goes for this particular philosopheme. But though I won't debate the point, I must in my capacity as philosopher give some reasons for my view. My view is a logical consequence of my view of debate in conjunction with my view of philosophy.
Debate is a game in which the interlocutors attempt to defeat each other, typically before an audience whose approbation they strive to secure. Hence the query 'Who won the debate?' which implies that the transaction is about attacking and defending, winning and losing. I don't deny that debates can be worthwhile in politics and in other areas. And even in philosophy they may have some use. Someone who attends, say, a debate between Willian Lane Craig and Lawrence Krauss will come away with some idea of what sorts of philosophical issues contemporary theists and atheists discuss. What he won't come away with is any understanding of the essence of philosophy.
Why is philosophy -- the genuine article -- not something that can be debated?
Philosophy is inquiry. It is inquiry by those who don't know (and know that they don't know) with the sincere intention of increasing their insight and understanding. Philosophy is motivated by the love of truth, not the love of verbal battle or the need to defeat an opponent or shore up and promote preconceived opinions about which one has no real doubt. When real philosophy is done with others it takes the form of dialog, not debate. It is conversation between friends, not opponents, who are friends of the truth before they are friends of each other. Amicus Plato, sed magis amica veritas.
There is nothing adversarial in a genuine philosophical conversation. The person I am addressing and responding to is not my adversary but a co-inquirer. In the ideal case there is between us a bond of friendship, a philiatic bond. But this philia subserves the eros of inquiry. The philosopher's love of truth is erotic, the love of one who lacks for that which he lacks. It is not the agapic love of one who knows and bestows his pearls of wisdom.
There is nothing like this in a debate. The aim in a debate is not to work with the other towards a truth that neither claims to possess. On the contrary, each already 'knows' what the truth is and is merely trying to attack the other's counter-position while defending his own. Thus the whole transaction is ideological, the two sides of which are polemics and apologetics. Debate is verbal warfare. This is why debaters never show doubt or admit they are wrong. To show doubt is to show weakness. To prevail against an enemy you must not appear weak but intimidating.
There is no place for polemics in philosophy. To the extent that polemics creeps in, philosophy becomes ideology. This is not to say that there is no place for polemics or apologetics. It is to say that that place is not philosophy.
Discussions with ideologues, whether religious or anti-religious, tend to be unpleasant and unproductive. They see everything in terms of attack and defense. If you merely question their views they are liable to become angry or flustered. I once questioned a Buddhist on his 'no self' doctrine. He became hostile. His hostility at my questioning of one of the beliefs with which he identifies proved that his 'self' was alive and kicking despite his doctrinal asseverations to the contrary.