Hard subjects seek out the doorway. The whole day was available, and yet the thing gets raised once a coat is already on, partly because leaving makes it feel safer to say. The other person then has to choose between being late and being dismissive, and whichever they pick, the subject is now attached to being ambushed rather than to being heard.

Pick a time and say you would like to talk then, even if the postponement is uncomfortable. Something that matters deserves a start rather than an exit.