Maybe where you live people don't get killed in brawls. There's a few people in Australia that
die in fist fights every year. And they're all grown ups, because grown ups have the strength and knowledge to kill someone, and kids generally don't.
I hope that you're never placed in a position where you
need to understand this. You've clearly never been threatened in a way that you actually believed that the other person was willing to try and kill you. But there are times when you have to recognise that while
you may be a rational, sensible person who can talk about something and walk away, that's not necessarily true of everyone else. Some people are emotionally unstable, and you can't always pick them.
Sure, you can walk out into the road and most people will stop for you. But every so often you'll get one driver who won't, or can't. How big a chance are you willing to take when the cost for getting it wrong is your life?
A police report is not a big deal, if you call the police and simply ask for their advice they'll probably tell you to file a report. Nothing will happen, but if things do escalate further down the line then you've got prior evidence already established. The threat implied by the police also goes a long way to dissuading people planning violent action, they know that you can't be bullied into holding your silence if they do decide to do something.
For some reason, Western society views using the police as cowardly. They're a tool to be used as appropriate, and not something to be ashamed of. When someone threatens your life, that's an appropriate time. If you can talk it out with the person afterwards, then great. But protect yourself first, because later it may be too late.