I think that's a pretty tough love type of answer from her.

It does make sense, if you think about it. In my opinion, it has to do with the fact that it's a different type of love (more like attachment) if you don't love yourself. I believe you can love someone else but your love will always have a part of needing to be taken care of that person in it, as long as you don't love yourself. It may not be obvious like in a child, of course, but you will expect things for what you feel (consciously or unconsciously) such as to give you more meaning or "complete you" (yes I don't believe that only romantic relationships can have that function) or you may want emotional support or whatever. If you do love yourself, you won't need that other person because you can fulfill your own needs, you have meaning even without loving that person, so you love that person because it adds something good to your life, not just to compensate for something you lack. I'm talking about need and lack in desperate terms, because on some level we all need something in any relationship.

I guess the way someone who loves themselves loves others is more peaceful and calm.

This isn't to make any suggestion or interpretation about your case in particular. don't know your situation. I'm just giving my opinion on the matter of loving others and yourself generally.