I feel like part of it is that she is naturally predisposed to the sort of disposition she ended up with, but this bit that went into her childhood already really pushed her into it.
https://dynasty-scans.com/chapters/my_dearest_nemesis_ch09#9
The thing with memory, for most people, is that it's usually inextricably tied to emotions. People tend to be better at recalling vibes, or at least how they felt than specific details, and those details tend to get fuzzier as time passes. And what are the things that provoke the largest emotional responses? Things we care about, things we are already emotionally invested in. Very simply, the things we don't care about or recognize as significant are the first things to be forgotten. So what happens when someone is primed to view people as a whole as largely interchangeable and ephemeral, as things that aren't worth investing time and feelings in from a very young age? You get Jiang as she is now. As far as she's concerned, her entire time in school was just her learning and maybe there were some people in the background while she was doing that.
And even then, I feel like she wouldn't have ended up in quite this state if not for Xu Qi latching onto her and making sure to alienate anyone who tried to get close to the brainy person she was leeching off
(she also seems to get a kick out of the act of driving wedges between people)
https://dynasty-scans.com/chapters/my_dearest_nemesis_ch11#8
Besides the well established bit with Shen, this page mentions ""friends"" and includes a different but completely faceless and therefore forgotten other girl whom I'm interpreting as someone else who tried to bridge the gap to Jiang despite her apparent coldness.
And Jiang isn't completely lacking in empathy, she just has some glaring blind spots. Basically, she has lived her life without attachment to people, and therefore fails to grasp when other people are attached to people. The completely cold, 'rational' thing to do if people are making you feel bad (whether by exclusion or whatever else) is to find other people. Jiang isn't grasping that it isn't the what so much as the who that really stung Shen at the time, or that other people who are emotionally invested in people can't or won't just walk away at the first notable set-back. But in the present she does pick up on the fact something she just said upset Shen in a major way, and so she tries to make up for it. But socially stunted as she is, she's only got one card to play.
Hah, guess I'm due for a reread if I can't even remember the previous chapters.