Why isn't the program outputting true regardless of case?

Question

My assignments requires me to keep accepting input from the user and output whether or not it is a palindrome until the word DONE is inputed. Also, words like Bob must have an output of true because we must disregard case (upper/lower.)

This is my first time using C++.

#include <iostream>
#include <string>
using namespace std;
int main()
{
string wordInput;
while (wordInput != "DONE")
{ 
    cout << "Please enter a word: ";
    cin >> wordInput;
    int wordLength = wordInput.length();
    int wordHalf = (wordLength / 2);
    bool flag = false;
    for (int i = 0; i <wordHalf; i++)
    {
        if (tolower((wordInput[i]) == tolower(wordInput[wordLength-1-i])))
        {
            flag = true;
        }
        else
        {
            flag = false;
            break;
        }
    }
    if (flag == true)
    {
        cout << "true"<<endl;
    }
    else
    {
        cout << "false"<<endl;
    }
}   
return 0;   
}

Answer 1

It might have something to do with 'wordInput' being declared twice, once right before the while loop and once within it. It is mixing up what the while loops condition is looking at.