Try this experiment: pronounce the vowels ㅜ (like “oo” in “moon”) and ㅣ (like “ee” in “meet”) one after another, reducing the time between them as they get closer to each other in the picture.
As you blend the vowels together, it will turn into the sound of the word “we” (which is romanized as “wi”): [You can see this without the animation]