Debaashish in India asked: What's the difference between "Why should I do this?" and "Why should I have to do this?"
The difference between these two questions has to do with the meanings of the two modal expressions should and have to.
Therefore, the first sentence (“Why should I do this?”) means “Why is this best thing for me to do?” or “What good reason is there for me to do this?”
And the second sentence ("Why should I have to do this?") means “What good reason is there for me to be required to do this?”
I hope this helps.