You can scientifically prove actions hurt with damaged/broken/burned objects, bruised/cut/burned skin, broken bones, or dead bodies. You can't scientifically prove words hurt. Actions speak louder than words.
Swearing is not just a teenager problem. Little kids do it and adults do it too. And it's not because they're stupid or unimaginative or lazy or because they have a low vocabulary. Most of the time, it's because they're angry. And they may have a valid reason to be angry.
If you want people around you to stop saying bad words, instead of complaining about them saying bad words, refrain from doing the following things:
1. Disappointing them
2. Disrespecting them
3. Pushing their buttons
4. Driving them crazy
Also, if someone around you is mad enough to say bad words, don't push that someone any further than you already have. That someone might escalate to breaking things or hurting people.