I don't know who came up with the phrase, "sticks and stone can break my bones, but words can never hurt me", but that person was at best gravely mistaken and at worst delusional.
Words are perhaps the most powerful thing in our world. I find support for this idea in the scriptures:
The creation narrative of Genesis involves God speaking to give purpose to all he has created.
John opens his Gospel by drawing a direct parallel between God and the Word of God.
Words draw their power from the fact they come from the essence of who we are.
When I say, "I love you" or "I hate you" or "I forgive you", I'm revealing the very core of my being - things that exist far deeper than the level of my intellect. It's conveying a part of who I am.
Matthew at one point records Jesus explaining to a crowd who believed that ritual eating laws led to holiness, "It's not what goes into your mouth that defiles you; you are defiled by the words that come out of your mouth." (Matthew 15:11)
Sticks and stones indeed...words are far more like weapons of mass destruction - or at least they can be.