He explains it from both points of view. How the dumper wants to appear 'nice' and not appear as a monster by being friendly with their ex. Constantly seeing your ex would be a continuous reminder of your guilt, then again they get to hang out with them and not have to 'reject all sexual possibilities in their name'.
He also looks at it from the 'rejected' party. Which he sees as being constantly reminded of a 'humiliating demotion' ignites hope. One isn't acquiring a friend, more an unwitting torturer," De Botton remarks in the video.
He also called trying to be friends with your ex a 'catastrophe for both sides'.
The best and most poignant point De Botton makes is how friendship after a failed relationship is used as a way to memorialise the former relationship, when what should be done is to maintain a 'far more honest state of civil distance'.