Mikomi is attempting to fire an arrow at Sojiro as he is emerging from underneath the bridge and Sojiro is attempting to use tunneling fang from beneath the bridge in both an attempt to dodge the arrow and deliver an attack at the same time.
As it is written, the ruling is that as sojiro emerges from beneath the bridge, Mikomi would use her sharingan to quickly locate the target, then fire at first sight. However, due to sojiro already moving up and forward, his body would no longer be where Mikomi fired her arrow, thus allowing him to dodge the attack, and move forward through the air.
The biggest flaw here is timing, when something was said and how it was triggered. View rp combat as a chess game, where each player gets to make their move, then the next player must react and make their move based on what their opponent has done. Mikomi's flaw was setting up a predetermined trigger.
Mikomi wrote:She waited patiently, she would fire the second he emerged. It didn't matter how fast he was, the Sharingan was faster, and her arrow was faster still. The instant she saw a flicker of him, he would eat an arrow.
So this sentence is where the flaw was made. The first issue here is the speed, as we have no real speed stat (speed is measured in movement, not reaction) The speed of the arrow and the tunneling fang movement would be very close to each other, meaning you can not use the speed of the flying arrow as a defense to out race sojiro's jutsu. The sharigan would allow Mikomi to quickly find and track sojiro, but that is not the issue here.
Again the problem is this sentence "she would fire the second he emerged." A predetermined trigger was set in place, saying the second she saw him, she would fire on him. However as he emerged, he was already moving forward and up into the air, the arrow would move to the location you first saw him at as he moved away from that location. Its tricky wording but what causes this attack to miss was the timing.
A better response to make the ruling in favor of Mikomi would have been to not say that you would fire on him the second you saw him, and to instead simply wait till he did reveal himself, then fired. The attack would have had a better chance of landing if you waited for his post, then replied that you tracked him mid flight and fired the arrow, leading him as you knew his location.
As a general rule of thumb, setting up a trigger like that normally back fires more often than working, because you are broadcasting to the opponent what they need to do to get hit, instead of reacting to their move. If Sojiro revealed himself, and stood still, the arrow would have hit. But because he knew that if he revealed himself, he would be fired upon, he was able to make a move that allowed him to move forward away from the arrows intended location as it moved towards that target.