I was under the impression that the etymology of disgust was quite obvious and well known. However, I was recently asked about it, and I realise that the connection might not have occurred to everyone. If you think of the word gusto, I am sure you will find it.
So, back to disgust. It came into English in around 1600, from the Middle French word desgoust, which was used to mean “strong dislike”. In Modern French, it is dégoût. Literally, the word breaks down as “distaste”. Let’s take a look at its two elements: des- and goust. Taking the des- first, it comes from the Latin prefix dis, meaning “apart, away” or also, as in this case, “the opposite of”. This element can be traced back to Proto-Indo-European *dis, meaning “apart, asunder”. The interesting thing is that this is thought to be from *dwis, meaning “twice”, from *dwo, which means “two”. The concept here is to express separation with the idea of “going in two ways”.
On to the second element of our word; goust. This of course comes from gouster, meaning “taste”, from Latin gustare of the same meaning. And here again, we can note something interesting. Gustare can be traced back to Proto-Indo-European *geus, meaning “taste, choose”. Perhaps the “choose” meaning evolved from the idea “develop a taste for”. And fascinatingly, the modern English word choose does indeed trace its origins back to *geus, via Old English ceosan. Thus, choose is in fact a distant cognate of disgust!