Here's why:
* Question is a noun and a verb, referring to a request for information.
* Interrogate is a verb meaning to question someone formally and rigorously, often in a suspicious or accusatory way.
* Ask is a verb meaning to request or seek something, often in a polite or informal way.
* Inquire is a verb that is similar to "ask" but implies a more formal or deliberate seeking of information.
All these words are related to the act of seeking information, but "inquire" best captures the formality and deliberateness that is present in the other words.