Give yourself an image of her that you can love or have compassion for. Maybe her as a small girl with scraped knees, crying. Whatever works for you. The picture should make you want to help her and be there for her, hug her for her sake. The image should also be strong enough so you stop being with yourself. Because that's what you do when you take stuff personally. And women are amazing at detecting a lack of presence.
When she says: I can't, she's trying to justify her fear, uncertainty and overwhelm. Last line of defense before the reactor starts melting. Because, if she can't, she doesn't have a say in the matter and therefore doesn't need to feel as inadequate. It's untrue, but "I can't" is easier than "I don't". Feelings usually don't care about reality.
On the other hand, if fear takes over, "I can't" may very well feel very real to her. The fear has to go before trying to cram more knowledge into her.
It's about the two deepest psychological fears: "I'm not enough" and as a consequence "I won't be loved"
So, start training. About 5 minutes a day, imagine her pulling off her defense mechanism and see her as the vulnerable hurt lovable woman. Train the idea that it has nothing, really nothing to do with you, it's just her hurt. And then imagine yourself doing the right thing. No blaming, no judging, just being there for her. In such moments, she needs your love and full presence much more than your coding skills, because when she feels uncertain, the topic is irrelevant and not the solution.
Not what happens decides whether you take it personally but how you interpret it. Training to meaningfully reframe the situation before it happens is the key to being able to do the right thing when usually you'd do the thing that feels right: taking it personally, feeling unable to help her, being in total reaction, etc. I call it autopilot. Reaction without sound strategy.
"It usually takes me more than three weeks to prepare a good impromptu speech." Mark Twain
Same concept.
It's all about emotional support. When she gets uncertain, you need to stop thinking of yourself as a tutor and start being trustworthy, dependable 100% partner.
As soon as the downward spiral even hints of showing up, you need to switch focus. Check thoroughly for anything that might make her feel less certain or less significant. Uncertainty is poison. Scale goes from 0 to 10 and she's close to 0. In such moments, she runs out of confidence juice. The brain hates that. Correcting her, making her try again when she feels she "can't", that'll all have to wait a bit.
After all, the coding skills should be a side benefit. What she really needs to learn and train is to trust herself again. Certainty is trainable like a muscle.
Every week get a few hours worth of practical psychology for a while. Books, videos. Then train what makes sense, more importantly, train what works. Women have different approaches than men. It's inbuilt and it's fine but you need to learn to play by the rules. The rules of her brain. And they don't teach those rules in school.
Be careful that you pursue the right goal.
Side note: How many times per hour does your teaching make people laugh?