Based on Aisha's testimony (she never saw the words at the top of the page), there are only 2 possibilities.

One, the words were added at a later time, when Adnan was alone and mooning over the old note from Hae. In this scenario, he's re-reading the note and getting angry, so he turns it over and then using the same pen (pencil?) he makes his declaration. Then he folds the note and puts it into a textbook where the police will find it later.

Two, the words were added at the very end of the exchange with Aisha, which is why they seem to be unfinished ("kill" is usually a transitive verb) and why Aisha never saw them. The bell rings, or the teacher hands out a test, or some classroom business interrupts their conversation, and he folds the paper, puts it into a textbook, and forgets about it.

For people who think the first option is more likely, my question would be why? "Because Hae ended up dead" seems to be the answer, but that's no way to analyze evidence.

In the Knox case, very similar assumptions were made about her plans and thoughts and motives after the fact of her housemate's death. She was innocent, but she was painted as crazy and sex-obsessed because that was what she needed to be in order to be guilty. (For example, much was made of a short story she'd written years earlier in which one of the characters was raped.)

It's at least possible that something similar is going on here, and it applies to much of the post-hoc "evidence." The note + the faking a catatonic state + the "all Asians look alike" comment keep appearing in lists of reasons to find him guilty.

That's not reasonable, imo. I'd also remind people who think SK was too glib with this that we DON'T KNOW whether or not she asked him about this. We only have the tape she chose to play -- so I'm guessing his answer was pretty boring, like, "I have no memory of writing that."