Actually, I figured it out. Your algorithm is going the wrong direction.
First of all, not sure why you are looping through the array when you know it will always have only 2 items. You can refer to those as arr and arr. Once you realize that, you only need to create a loop which loops through each letter of arr and see if that letter is somewhere in arr. You are on the right track using indexOf, but you only need to be using it on arr and not on both.
Whenever you are unsure what a specific line of code is doing, console.log() is your friend. I was going to try to explain why your code shows true for everything, but it was complicated and I felt it was better to point a few mistakes out and get you started in the right direction. If you need more help or hints, please feel free to ask.