In simple terms, it is because the letters with the umlauts (“ä, ö, ü”) have a different pronunciation (i.e., with an “e” sound superimposed on the basic sound) than the same letter without the umlauts. The umlauts you see, which consist of two dots, originally were the tiny German script letter “e,” which was written as in the following illustration:
When a letter, such as “a,” “o,” or “u” was to be pronounced differently, an “e”:
was written over the letter. This letter “e” gradually, over time, was reduced to two vertical strokes,
and eventually to two dots. And that is the way the umlaut developed in German writing and printing.