Why can't I ...?
is perfectly correct grammar as far as I can tell. But what happens if the contraction is removed,
Why cannot I ...?
This sounds bizarre, but would this be technically correct grammar?
Why can't I ...?
is perfectly correct grammar as far as I can tell. But what happens if the contraction is removed,
Why cannot I ...?
This sounds bizarre, but would this be technically correct grammar?
When you remove the contraction, you need to say:
Why can I not...?
just like with the auxiliaries do or have
Why do you not continue...?, Why have you not completed the task?
YourDictionary explains:
In question form, the noun or pronoun comes between can and not. For example:
- Can we not discuss this today?
Note that can+pronoun+not+verb sounds formal, even somewhat dated in certain contexts. The KJV Bible uses it:
... can ye not discern the signs of the times? (Matt. 16:3 KJV)
Also, this formula helps when you want to emphasise the NOT.
Cannot used before the subject in rhetorical questions is possible, but not that common. You will find it in books dating from before 1850's or in poetry (see Googlebooks).
When forming question, the auxiliary verb is moved to the front of the clause from its normal position:
Not can only move from its normal position if it's stuck to this auxiliary. It's the auxiliary that's carrying not round to the front of the sentence. It can only do this if they're joined together.
If not isn't contracted, it must stay in the same position it has in a normal declarative sentence. Below the parts that invert are in light font, the rest of the sentence is in bold. In sentence (3) we see not moved away from it's normal position because it's attached to the auxiliary verb. It's sandwiched between the auxiliary and the subject:
The examples above are yes/no questions for simplicity, but exactly the same things holds in open questions like the OP's too.