When she says, "You HATE ME!", she may be using that in a number of ways:

- She needs reassurance, and this is a quick way to try to get it.
- She's angry and lashing out with a verbal WMD.

You kept your calm, and extricated her from the situation. I wouldn't have tried to handle it any differently. The only advice I can offer on how to stop the cycle in the future is to be ready to end the activity sooner, before it escalates to the same point.

In case she's trying to weaponize it, I can only recommend that you not show your DD how much hearing "You HATE ME!" bothers you.

As for framing the conversation, the problem here seems to be one of unrealistic expectations. Your DD will often find things confusing. Some things take time to learn. We often need to have information presented in more than one way, before something clicks. Sometimes we need additional information that hasn't been presented. Sometimes we just need time to process what we've learned, in order to put it into practice.

When this topic has come up with my own DD10, I was able to offer her my own professional experiences with difficult problems that weren't offering themselves any solutions:

- When things don't make sense, my frustration can build, which becomes an enemy to clear thinking. Also, sometimes my thinking is just plain wrong, but in the moment I'm locked into that bad logic path. In both cases, a key trick is to WALK AWAY, and stop thinking about it for a while. Even in high-pressure situations, I've found it helps to leave the room, grab a beverage, go find someone and talk about their day. After some minutes have passed, I come back in, and take a fresh look at it. It's often times that this fresh perspective shows me my error, I laugh at myself for missing something obvious, and that ten minutes away pays off in spades.

So, your proposal to come back to it later was a solid strategy used by a great many smart people, and your DD should give it a try.

- Sometimes when I use the above trick, the other person ends up drawing me out to talk about the problem that drove me out of the room, even though my purpose was to think about anything but. Even if they're someone who has no background in what I'm working on, the process of explaining it to them so they can understand enhances my own understanding, and once the problem has been given full explanation, the next steps tend to present themselves.

This ends up as a one-way conversation, with the other side limited to, "Oh." "Uh-huh." "Yep." "Uhhh.... you're welcome?"

I've been on both sides of this conversation. It's rather common in my world.

- And then, of course, there are the conversations with someone who knows what I'm talking about, which very often leads to helpful information, because they've dealt with something very similar, and they may have tools or strategies to offer that you've never seen or considered before. These then become part of your permanent toolbox, helping you grow. Learning from other people is ALWAYS a good idea.

- For some even harder problems, I've seen where considering the problem in idle, random moments often leads to breakthroughs. To illustrate this, I describe one of my most brilliant coworkers, who would announce a big idea to a problem that had been perplexing us for weeks with the prelude, "I was in the shower this morning, and..." It was amusing and disturbing at the same time to hear so often about his showers.

- I've also mentioned the neuroscience of how people process information in their sleep, and the thing which was difficult the day before, becomes obvious and easy the next day. So, when time is not a factor, "sleep on it" is solid advice. DD has seen this in practice, where that gymnastics move she failed on 50 attempts one day, she nails it first try the next morning.

The overriding theme here is that this is how really bright minds work on difficult problems. Nobody gets all the answers right away. Forcing yourself to get the absolute right answer immediately can actually be counterproductive.