HATE is such a strong word

A couple of days ago my 5y looked at me and said "You hate me." Because I wouldn't let her play with something she wanted, or have a snack at that moment, or... something.  I don't even remember.  I said "I most certainly do not hate you."  She said it a few more times and we went back and forth until I realized we were not going to get anywhere.  So I asked her if she knew what that word meant.  She said "no".  So I simply explained that to hate her, meant I wouldn't love her anymore.  And I definitely love her, no matter what.  She said okay, and went into "You don't like me", which I could handle.
A day or two later she looked me in the face and said "I hate you" (because I wouldn't let her watch her TV show).  It pained me to remain as calm as I did, but I didn't take offense.  I just kept repeating to her that it doesn't matter how she feels about me, I will always love her.  I feel like this is the best possible option for a situation like this.  Right now is when our children are forming their opinions about the world.  And in this particular instance, about love and relationships.  Even about marriage.  They are watching EVERYTHING we do.  When I tell her that I love her even if she hates me or even when she's naughty, she learns about unconditional love.  Love, real love, is more than a fuzzy feeling.  It's a choice.  It is choosing to care for someone even when you don't "feel like it".  And I choose to love her no mater what.  Call me crazy, but I think something like this sets the foundation for relationships for the rest of their lives.
Eventually she calmed down.  She even said she loved me later.  And much later, when we were all in good spirits, I told her that it hurt my feelings when she said she hated me, and I would be happy if she didn't say that again.  She said okay and went about her business.  And then the next morning, after she had had some time to think and digest, she came to me all on her own and said she was sorry for saying that to me.  I said "Thank you" and dropped it.  There wasn't any more to be said about it.