So while Kazaa and the like eventually got the ability to actually download from multiple sources, and be able to see that a particular source is popular, as I recall from the early 2000 days, back then it was pure point to point. That is, if you chose to download something, you also were implicitly choosing what source to download it from. So even if five people had the file "Foo", you chose which one to download, and there was no way to know that 4 had the same file "Foo", and 1 person had something else, with no way to know which was what you wanted.
Torrents avoid many of those issues; you can see how many seeds a file has (though Kazaa and the like later added that). And you had to have gotten the magnet link from somewhere, which would have its own evaluatable trust. It's the difference between downloading file called "Foo" from random internet user's computer, and going to a website, that you know, and downloading a file called "Foo" that you also know has been downloaded, and retained, by X number of users.
Torrents avoid many of those issues; you can see how many seeds a file has (though Kazaa and the like later added that). And you had to have gotten the magnet link from somewhere, which would have its own evaluatable trust. It's the difference between downloading file called "Foo" from random internet user's computer, and going to a website, that you know, and downloading a file called "Foo" that you also know has been downloaded, and retained, by X number of users.