Thing about BPD is the reactions usually don't come out of nowhere, but are overreacts. I am now going to try to give the most basic example as I can.
Let's say the guy is with someone he loves and feeling all mushy and relaxed because of it. Then this loved one says something in the lines of "Did you forget buying lemons?" A BPD mind goes into a spiral of "What are they implying! Am I that terrible of a human being! I forgot lemons I am so useless! Wait do they think I am useless? They are mad aren't they? It's just lemons I don't deserve this how dare they be mad!" and start yelling. This entire spiral happens in a split second, and that's why you usually don't see him start to fight before he starts yelling like that. So a brief explanation of which nerve it hit - but make sure it's a very brief one so pacing does feel like like it happened in a split second, can be just enough.
But the key is that the spiral is purely emotional - as you can see in my very amateur example, the steps are brief sparks of emotions tying to another, and no pausing to think about what the other person actually said and in which tone. In that split second, due to the rush of all the hormones, the guy with BPD has a very narrow view of things, not properly judging any outside factor.
You could write this particular example as:
Looking at his best friend, moving about to fix this and that, filled Daniel with a sense of peace he didn't expect to feel. Everything was normal once more, and Jack going in and out of kitchen to prepare a meal assured him of the fact.
Jack stared at the contents of the fridge for a second. "Did you forget buying lemons again?"
All that peace evaporated in Daniel's mind. "So what?" he yelled in response, curling his fists. Jack had said again. He was exasperated, wasn't he? Exasperated with Daniel, over fucking lemons, after everything they've been through. "Is that your entire problem? That we don't have enough lemons to stick up your ass?"
Of course, part of it is also that you've already established your character as BPD or at least with its symptoms. If this were the beginning of the book, Daniel's outburst would still look out of place, because we don't know the character and his inner workings, but brief mentions of why Daniel thinks he's right to react the way he does in that moment ("Jack must have been sick of him but over this shit? Really?") will make the reader go "huh."
Now if you ask about how to establish it in the first place to get it to that point, it's just writing tricks. During the getting-to-know-the-character parts in the beginning of the story, have him give reactions like this in situations where pace is slow so you can throughly explain the spiral. Anger and joy tend to be quick and need quick pacing, but you can use longer-winded emotions like sadness or happiness to ease the reader into the concept. For example, the trigger comes in the form of a visual - perhaps a light turning red just when he was about to cross the street. It reminds him of missed chances or being unlucky, and his cheerful mode drops due to remembering these as he thinks about how this is a metaphor for his life (even though it really isn't one). You can extensively explain his being depressed for the next half or couple hours, giving you enough time in narrative to introduce his snappy thought process.
