Your problem with self-compassion: the one that leads you to be kind and supportive to other people, but nasty and vindictive to yourself. One reason you struggle with the 'self' part of 'self-compassion' is that you view yourself as separate from other people. But what if you aren't? What if the gap between you and others is simply too small and inconsequential to support your difficult-to-shake belief that it's wrong to be nasty to people, unless the person you're being nasty to is yourself? Your imperfectionist friend is lobbing a giant metaphysics truth bomb that is going to blow apart your conviction that compassion is for everyone except you.
Find Kristin Neff's website about self-compassion here.
Reference:
Parfit, D. 1984: Reasons and Persons (Oxford: Oxford University Press).
The Academic Imperfectionist