I am not even denying the idea of focusing on a point. What you are forgetting that it depends upon the eye's line of sight. In ALL occasions or examples you have spoken of, the second another object occupies the point established in the line of sight, it would ignite in its place. What the eye cannot see it cannot ignite. You HAVE to consider this point on all the basis, as this is the actual point of confusion here. What the object is out of focus, and out of its line of sight, what would the eye ignite?Focus has everything to do with it, the argument that I'm countering is that Amaterasu instantly ignites where the user is looking. I.E. If you're looking at that dot on that piece of paper then it's going to combust, that's the argument some people are making.
However, let's say that there is a table under the piece of paper. My first argument is that if you move the paper with the dot on it then Amaterasu should simply ignite the table since the focal point changed, a fireball should not be shot at the table simply because the paper with the dot was removed.
My second argument is that, if Amaterasu will ignite the dot on the piece of paper, then it should be impossible to move the piece of paper out of the way. You can't avoid something that's instant.
Thirdly, if you put your finger in front of the dot, Amaterasu shouldn't just turn into a fireball because it's focal point was blocked off... the finger is the new focal point, so it should combust. Alternatively, if Amaterasu was used before you covered the dot with your finger, then the dot should still combust regardless of the placement of your finger.
Except when Itachi used it against Sasuke, or when Sasuke used it against Ei.
You have misunderstood Itachi's intentions then. He never wanted to kill Sasuke. Hell, he even made a hand-seal before using Amaterasu and kept his vision in Sasuke's Wake, as Amaterasu follows the eye's line of sight. In case of Ae, you HAVE to look at another factor; Ae pumped Bijuu level chakra into his V2 cloak to dodge Amaterasu. He has never done that on any occasion and side stepped it when it was just spawning. It all happened extremely quickly. Look at the Flame; it's exactly on the spot where Ae left his flickering image, only that it's a bit bigger then.