People curse in two ways. Either they take holy names ( God and Jesus Christ), holy activities like sex, or body parts created by God, and use them to exclaim common emotional responses, or to degrade another person.
All of these things are what God has called holy, and so to curse is to make holy things common. More on God's name here
Often people use cursing when they feel unempowered, threatened or inferior.
If I am a child of God, I never need to feel threatened or unempowered by any one or any situation as all power has been given to me in the natural and supernatural realms.
I can be humble in all circumstances because if God is the supplier of all things in my life then I have no things or pride that can be threatened by others.
Verses to consider on this topic;
Psalm 68:35
Romans 15:13
Eph 4: 29 ...let no corrupt talk come out of your mouth...