Obito unlocked the MS. kakashi's eye happened to be connected to obito's so his was able to transform into MS as well.
Simple as that. Don't over think it or over complicate it.
Connected through sight, not through chakra. That's Obito's chakra wouldn't be flowing into Kakashi's eye to make it in the MS, it's that simple. Sasuke's eyes are connected yet Sasuke shown 1 of his eyes can improve over the other
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. How can Kakashi activate his MS from his Sharingan? It takes the same chakra to active it so Kakashi shouldn't be able to use it at all in your logic.
.... look closely at the blood trail his eye blood isn't even connected to the forehead blood. It came from his eye.
Look at the top right pic, no blood until the blood from his forehead went to his eye and started to drip. When you cry the tear usually come from the end and the rain had water going down his face so the blood only carried to the end of his eye. He has no reason to bleed since as you can see it's his normal eyes and no MS. His eyes only shown to bleed when he has MS and using Amaterasu so unless you see his MS and Amaterasu he didn't awake it.
When he used Amaterasu on Obito it took the shape of Itachi's MS, not Sasuke's. Did we see Kakashi and Obito bleed when they get MS? No but we saw their MS. Sasuke wasn't using Amaterasu to bleed and it wasn't for awakening something that he haven't even shown.
But he unlocked before obito even got to explain the truth bout itachi cus as soon as sasuke saw obito he used amaterasu
That was a 1 shot Amaterasu that Itachi planted in Sasuke, it took the shape of Itachi's MS, not Sasuke's.