I am not sure what kind of fallacy is involved in the last line of this dialogue:
"Will you go to the mall with me today?"
"Why should I?"
"Why shouldn't you?"
I think it is a complex question?
"Will you go to the mall with me today?"
"Why should I?"
"Why shouldn't you?"
The response seems to be making an appeal to ignorance: unless you can prove that you shouldn't go, that one then has proof that you should go. Obviously, not being able to list why one shouldn't go tells us nothing about why one ought to go. For example:
You have no good reason not to marry me, thus you should marry me!
The fallacy is more obvious in this example.
A complex question requires you to assent to something that is by itself questionable. For example:
When did you last beat your wife?
This question presupposes that you beat your wife.
Did you wire the water pump for 120 volts or 230 volts?
This second example assumes you wired the water pump yourself and not someone else. In both cases, the question has a different structure than the one you are asking about: answering it doesn't commit you to something dubious.