Because while the United States federal government does not declare a de jure official language, English is de facto the standard language, as all laws and regulations are published in at least English. Further, virtually everyone in the US speaks English and many don't speak any other languages. For example, I have three years of Spanish, but I can't understand spoken Spanish (I'm better with written Spanish).
If someone does not speak English in the United States, then they will likely have issues doing such basic things as ordering takeout or hiring a taxi. Or doing more esoteric things like going to a politician's town hall or chatting up a potential romantic interest in a bar.
So English is the unofficial language of the US. And as such, is a requirement for immigrants to be naturalized, as otherwise they couldn't integrate into society. They would be perpetually separate and limited in the society they keep.
As @jamesqf notes the literal reason is that Congress passed laws requiring English speaking for naturalization and did not pass laws declaring an official language (or languages). Presumably the reasons why they passed such laws is for the reasons that I stated.
Congress has never been able to agree on the need for an official language. So while English is the obvious choice, it has never been officially chosen by the federal government. Some states have chosen to make some set of languages official in that state. English is always included.