It means the person is stubborn. They won't meet you in the middle.

when we say (give him an inch)it means...Be generous to someone and the person will demand even more. for example If you let Mark borrow your tools for this weekend, he'll wind up keeping them for years. Give him an inch and he'll take a mile. Conversely, when we say to someone (you don't give an inch) that mean this person is Difficult to deal with him or Uncharitable one .

You say this to another person when you are arguing with them and they won't consider your side of the arguement or You hope to have someone change in some way and they won't (they are stubborn).

It means Eliot doesn't even have an inch to give. :P