It is actually impossible, by definition, to teach yourself anything.

Teach: to impart knowledge or skill

Impart: to make known, tell, relate, disclose

You cannot disclose something to yourself that you do not already know. That would also imply that you can consciously choose not to disclose something to yourself. It doesn't make any sense that you could have knowledge but still need to learn it.

What people who use the term "self-teach" actually mean is "self-study." The knowledge comes from outside of them. And there is a major issue with that.

There are perhaps a handful of acceptable techniques in playing the violin, and there is really only one ideal way that maximizes potential and minimizes injury. There are thousands of ways to vary from these acceptable sets of techniques, and any variation is going to result in serious injuries and limited progress. Anyone can post a video on YouTube. The vast majority of violin "tutorials" demonstrate several examples of bad technique. If you follow them, you risk damage that will prevent you from performing daily tasks. There is a reason the Journal of Hand Surgery and others have used violinists in research projects and as textbook examples of things like carpal tunnel. The tradeoff of the money you save by not taking lessons just isn't worth it.

And it is not those of us who insist on proper lessons who are discouraging those who want to learn. Quite the opposite, in fact. Those who make the violin sound like it is something you already have in you (or perhaps don't have in you) and report that it is easy to figure out on your own are actually discouraging those who don't see immediate progress - which is going to be virtually everyone who doesn't give themselves the best possible start. The result is that they will buy a cheap, unusable violin that will sit in a closet gathering dust until the sell it at an even cheaper price to someone with just as unrealistic expectations. That is a tragedy, and it is best addressed by giving people a dose of reality so they will not set themselves up to fail.

With each passing generation, we have seen a decrease in a skill called "delayed gratification." That is the ability be content when you can't have what you want immediately. Technology continues to increase the speed at which we can get what we want, so we never learn how to wait. So if you are, say, over thirty, you are one generation better at delayed gratification than the OP. If you are over fifty, you are two generations better at it. A fourteen-year-old, with the exception of those with parents who severely limit screen time and only buy new toys for Christmas and birthdays, has no chance of developing any sense of delayed gratification in our society. Those who are children now will, even as adults, want everything right now or else will lose all interest. They won't have the patience or the attention span to study anything on their own because they won't know how to build structure that is not provided for them. They will have no direction and no sense of purpose unless someone teaches it to them. This is why we have so many unemployed young adults with advanced degrees. Formal music lessons in any instrument, complete with recitals and competitions, can provide a sense of purpose, even if that purpose later turns out to be something other than music because it teaches students to set goals and achieve them before set deadlines. Studying one instrument formally and using another essentially as a toy chips away at any life-lessons being gained from formal instruction because it undermines the necessity of such instruction.