Yes, you can teach yourself chess. Playing chess alone will improve your playing strenght up to a certain level. Let’s say you run against an invisible wall if you only play chess but do no further studies..So playing by itself will not really improve you to a large extent. You will just stop blundering away your pieces, but that’s it.
1. To really get better at chess you need to study chess books about how to conduct a game correctly. This means you have to study chess strategy and chess tactics on a regular basis with books or videos.
2. Make sure you study positional chess very deeply to improve further. You should know how to handle different kinds of positions.
You can’t learn all those things by playing only. If you only play chess, but do no studies, then you will play the same nonsense for the next thirty years to come. It is that simple.
I personally met many chess players who never studied any chess books and I observed their playing style over thirty years later. They had not improved at all, but played the same crap as before.
A player wrote me an email saying that he hates endgames. Before he reaches the endgame he offers a draw. Fact is, when you never play endgames because you don’t like them, then you will never learn how to play an endgame. Simple logic.