God’s choices being constrained by His nature doesn’t amount to His choices being entirely determined by His nature. The difference between constraint and determinism can be described with a more physical case: The shoulder socket constrains how far and in which directions one’s arm joint can move (without really getting hurt anyway), but it would be silly to say that the socket itself ‘determined’ which directions one’s arms moved and when, since the joint moves freely within the range of the socket. Likewise, the constraint that God cannot lie doesn’t preclude Him from having other options, since choices don’t always come down to only the two options of ‘be dishonest or don’t be dishonest;’ there can be more than one choice within the range of honesty and Holiness.I think this is a helpful analogy for Arminians to use in explaining their position.
While it is true that actions have consequences and thus certain choices make others logically impossible—if one muscle on the shoulder contracts to move the arm then for movement to occur other muscles must relax—the constraint of possible actions does not prevent all choice. Free will means that we can make real choices within limits of the ability we have been given.
Note also that some choices will be theoretically possible but may be limited in some men by their lack of awareness of the possibility.