So in the last minutes of the episode 16 Kaori (while in bed) tells the next thing to Kousei:
"Want to commit double suicide with me?"
I know for the dubs it can be a little bit off and the real meaning can change, so i read more about it and I think the meaning can also change from "double" to "lovers"; "lovers suicide" in the Japanese culture is used to describe the practice of lovers to suicide (da) when they couldn’t get to be together and marry for social/familiar reasons.
I am not sure if I am doing right by bringing this now, but I can’t let go the anime, even I don’t know why I am holding this hard to it.
So I have a theory here and this is going to sound harsh and maybe cruel, but I believe that this line: "Want to commit double suicide with me?"Was a declaration of love to Kousei. And the more I think about the more it makes sense (or so i want it to make): the not "fitting" into Kouseis Group of friends(social circle), Kaori didn’t wanted to destroy the relationships between Kousei and Tsubaki as she knew she was not going to be around for much time, and by saying it directly to Kousei she loved him, at the end she would had only teared apart his heart (driving him into a bigger grudge) so by saying to commit suicide with her I think she was saying: "I love you, but your heart will die when I die"(ending his life as well, o so I believe). I know they where 15 years old, but who knows, maybe Kousei got the memo and understood, explaining why he doesn’t cry when reading the letter.
Tell me what you think. And thank you for reading. XD here take a potato.
Shigatsu isn't the only anime that mentions a suicide pact between lovers--Kimagure Orange Road comes to mind, although that was a case of plain misunderstanding. I think Kaori was just referencing Masahiro Mita's Ichigo Doumei--if you look carefully, you'll see a copy on Kaori's wheelchair. Just as Kaori quotes from Charlie Brown, she also quotes from Ichigo Doumei, specifically Naomi, Ichigo Doumei's tragic heroine. Naomi also says "Let's commit double suicide" to Ryoichi, the piano-playing protagonist who parallels Kousei. She also quotes Naomi again when she says “You really are a strange person. You came to the hospital to visit me, and yet all this time, you haven’t said a word?”
As for not crying when he was reading her farewell letter, I think it was a sign he was coping with the sorrow--the pain might never completely vanish, but he will emerge from the experience stronger and wiser, and one can hope his music will become more beautiful, colored as it is by sadness as well as joy. And though it, Kaori will also still live, because like they said, "I exist in you," and the memory of their days together will inform, mold, and shape each note Kousei has yet to play.
I don't exactly think that was the intended English translation. At least, in the sub that I watched, what she said was "Would you like to come with me to see how it all ends?" I can see how that can be taken in a darker way but in my opinion, I think it's more beautiful to think that Kaori knew she didn't have much time left and wanted to spend the remaining moments of her life with Kousei. I feel that she was asking if Kousei would accompany her in the last moments of her life and THAT seems much more meaningful and beautiful.
EDIT: I wrote the last comment and wanted to expand on it XD
This idea that Kaori would suggest a double suicide really bothered me and I decided to look deeper at the details and I totally agree with Bellumfuriam.
Whenever she would quote a fictional character (ie. Snoopy, Charlie Brown), the subtitles would have quotes around these phrases. Picking this up the first time I watched, I did notice the quotes around the last lines of episode 16 but was confused as to why. Now, knowing the context of the situation, I think the best explanation is that she was quoting the book (that the anime zoomed in on specifically) near her bedside. Logically, it makes sense that NO 14 year old would have such dark thoughts. However, maybe this was her way of expressing her love to Kousei as the original post suggests. She clearly liked to use quotes from other characters as metaphors and maybe this was her roundabout way of expressing her love without explicitly stating it.
I understand how in the Japanese culture a lovers suicide or a double suicide is romantic and why a couple would be led to do so. However, I don't think this would fit Miyazono's personality at all, especially looking at how positive and kind she really was with others. In my opinion, if Kaori truly loved Kousei, she would never want to do him any harm, especially not for him to kill himself.
Overall, I think the final lines of dialogue was simply just Kaori quoting lines from the book by her bedside (as explained in the first comment) as a way of expression rather than suggestion. I think that Kaori would never want to harm anyone, especially not for her own selfish reasons. Thanks for reading and I hope you have a wonderful day!