Embarrassed!

I just had breakfast with my parents at Denny's and I'm embarrassed. I need to know if I'm overreacting. We were sad behind a man and I'm assuming his teenage son. The boy was probably between 14 to 16. We were eating and we could hear the dad trying to make his son eat and the son was saying no. The dad was saying "I'm not going to let you starve." "Please. I need you to eat." Son kept saying he doesn't want to eat. Dad is basically begging his son to eat. They weren't being loud. We were just right behind them so we could here. My dad turns around and yells at this kid "Fucking listen to your dad and fucking eat! You're being disrespectful." The dad said "I appreciate the help, but plz don't talk to my kid like that and mind your business." My dad said back his day he would have gotten a switch to the ass and food shoved down his throat. The son got up and ran out of the Dennys and dad said fucked and ran after him. I was so embarrassed. I wanted to die. My dad was saying parents let their kids run all over them these days and starting complaining. I could see the father son duo from the window because they were talking outside and I honestly think he may just have something going on. Idk what that something is but it just seemed like the duo was maybe going through something. The whole thing was just embarrassing and I asked their server if I could pay for their food. It's honestly not really a big deal when I think about it.