My understanding is free radicals are literally atom sized bombs. Bombs are trouble because they lead to dangerously quick oxidation, transforming a solid into a gas in milliseconds.

Now consider you are a cell. A lot of things you consider important are individual molecules. Free radicals are oxygen ions. So get a few of those ions inside of you and your important molecules are getting oxidized. They’re getting ripped apart. The same as a grenade in a trench. But at the indivisible scale.