grammar: why do we or omit the "do" [duplicate]

Solution 1:

No, you may not omit the do.

A question headed by a Wh- interrogative (who, whom, whose, what, which, where, when, why, how, and a few others) must have a finite verb in the second position^†; and that verb must be either a form of be or an auxiliary verb.

indicative:       interrogative:   
He is right.      Why is he right?    ... the finite verb IS is a form of BE  
You must fight.   Why must you fight? ... the finite verb MUST is a modal auxiliary  

But if the finite verb in the clause is not one of these, then it must be replaced with a do construction (this is called 'DO-support').

indicative:       interrogative:   
You fight.       *Why fight you?      ... wrong: FIGHT is not an auxiliary
                 *Why you fight?      ... wrong: there is no verb in second place
                  Why do you fight?   ... right: DO is an auxiliary in second place.

A tricky piece is that do and have (and a few other verbs) may act as either an auxiliary or as an ordinary lexical verb. You must be careful to employ do in the second case:

indicative:       interrogative:   
They do wrong.   *Why do they wrong?      ... wrong: DO here is not an auxiliary
                  Why do they do wrong?   ... right: the first DO is an auxiliary
He has a car.    *Where has he a car?     ... wrong: HAS here is not an auxiliary (but
                                                 this was at one time acceptable)
                  Where does he have a car? . right: DO-support provides the auxiliary

^†Second must sometimes be loosely interpreted with which, what and whose; if used as adjectives these are followed by the NP they modify, as in What courses are you taking?
* before an utterance indicates that it is not ordinarily acceptable