The sound of an Old Italian violin is a part of the culture that is quickly disappearing. Just like other things of a fine nature, its subtle qualities are not obvious, and have to be pointed out to be appreciated. Not many students are lucky enough to meet a teacher who would help them to discover the beautiful sound of the Classic Italian violin. There must be a most unusual set of circumstances to present this kind of knowledge to a person on their own. Unfortunately, the majority of young violinists don’t have such guidance, and are mostly consumed with the technical challenges of the instrument. They listen to the old masters or a competition only to hear the technical part of a performance. The quality of the sound is the last thing on the mind of young violinists, and is pretty much ignored at this stage. Consequently, developing a good tone is practically impossible especially when one doesn't know what it is. Furthermore, it's only fair to say that most of their violin listening experience is happening from close-up, almost from inside a violin. Unfortunately the intended effect (the sound as it is perceived from the audience’s point of view) is not audible to the performer, and is very difficult to evaluate properly from his/her position.
It would be a safe bet to say that most violinists would not recognize their own violin being played by someone else, despite the most intimate knowledge of their own instrument. In other words, most violinists don't know how their own violin sounds to the listener, just as we ourselves are surprised at how our own voice sounds played back on a tape recorder.
A good violin doesn’t sound good only because its strings are touched by a bow.
There is no mystery in the fact that the same instrument played by different people produces different quality of sound. The reason is (besides the obvious - different technique) that people themselves sound differently. Just like with brass players, where every player has their own unique sound regardless of the trumpet they use (different muscle structure, bone density, different mouth shape, lung volume, etc.) By the same token, all violin players also sound differently, and the big part of finding a ‘good’ instrument is to find a violin that complements the player.