You might have been interested in continuing the conversation if the other person didn't descend into trash-talking first. I think that's the message the author is trying to convey.
But I agree with you that "I can't continue this conversation" is probably not the best way to respond, even in that case.
This person has been let go and you're reaching out _to them_.
If you don't care about the person and their emotions, don't say anything. Nobody else will know otherwise (other than the person you clearly don't actually care about). Feigning care is sometimes worse than just clearly not caring at all.