At some time or another, most learners of Korean have likely heard native speakers say 가리키다 (to point out/ indicate) when they meant 가르치다 (to teach). The confusion of usage is relatively easy to understand in context and poses no serious challenge to understanding if one knows both words, but why exactly do Koreans sometimes confuse the two?
The answer can be found in the origins of the two words. They actually originate from the same root and share a common meaning. The word "가르치다" originally had both senses of "teaching" and "pointing out," although today the two meanings have split into different words which are used independently of one another.
The root of the words 가르치다 and 가리키다 is "갈," meaning "to split up (and thereby distinguish something)" (as in 가르다 "to split/ divide" and 가리다 "to distinguish/ select," both from the same root). To this root is added "치다," which in this context means raising, rearing or cultivating. An example of this is the word 양치기 which means "shepherd/ shepherding." Likewise, 가축을 치다 means "to raise livestock."
This dual meaning of "distinguishing/ pointing out" and "raising/ cultivating" within the word 가르치다 makes it clear why Koreans sometimes use 가리키다 instead, and also reveals the common origin of both words. When Koreans use 가리키다 to mean "to teach," it's because they are making a connection between 가리- / 가르-. However, as I mentioned earlier, the two meanings are separate in modern Korean and learners should be conscious of this when learning the two words.
백문식. 우리말 어원 사전. 1st ed. 서울: 도서출판 박이정, 2014. Print.