Earlier quoted context omitted.
To be fair to your mother, this particular advice and view was rampant when I grew up in the 80s/90s. My experience was that this is quite backwards. Physical altercations at school didn't hurt that much, but the name calling, social shunning and constant verbal put down was very painful and has affected my whole life.
It's incredible how common the "it's just words" refrain is on HN. Wars happen over words. Marriages and divorces too.
Words are not the cause of these events. They might, in several ways, trigger them, of course. After all, a declaration of war is nothing but words and so is a legal divorce filing.
However, for these and other conflicts, if we dug down to root causes, we always find a lot more than just spoken or written words. Two that come to mind would be, in the case of war, strategic/national interests and, for divorce, infidelity or serious lack of agreement on matters the couple deem to be important.