- Damnit, now this troper's never gonna see the movie in the same way. Thank you, good sir.
- Oh..my god. I can (unfortunately) see that happen. True Art Is Angsty, huh? Well I feel A LOT better....
- You... I cant... I lived something similar, and this could be true. Thanks my man
By the third part of the movie, Takaki quits his job and leaves his girlfriend of 3 years. He likely expected his job and relationship to make him happy, but his depression kept him from really enjoying either; he's still stuck in his own head just like in high school. So, he walks around aimlessly instead. Only after he sees Akari does he start to have a slight bit of hope.
- One more side mentions that he had thoughts like wondering what the world would be like without him in it, not an uncommon thought for those with depressive symptoms, and he also had inexplicable urges to cry and loss of interest in activities he used to like. He therefore does indeed have depressive symptoms at minimum.
The idea is that the Akari that Takaki saw at the end was either a hallucination or an Identical Stranger/stranger he just mistook for her at a fleeting glance. Thus, her not bothering to wait for the train to pass. If it's a hallucination, then his letting it disappear also ties in to his letting go.
In all frankness, even if they were no longer romantically involved, the idea that one wouldn't wait to greet a long-lost old friend... Well, the theory that the woman was not actually her is slightly less depressing than their relationship having fallen so far apart that she won't even wait to exchange greetings as friends.
Supporting this are the lyrics of "One More Time, One More Chance", playing over this scene, which strongly imply that the her he sees is but a fantasy in his head: