I agree with this.
OP, she isn't their friend, they are yours. Maybe she already suspected this and maybe it's a dawning realisation.
I'm not saying the following is necessarily true of, or definitely applicable to your girlfriend, but just as an illustration of how these patterns can emerge.
It's likely there is a reason for this stemming back to her childhood. Either trouble in the familial relationships; friendships troubles at school and patterns of behaviour she recognises from previous romantic relationships. If this is the case, it's likely to be more than one of these. Especially if the issues stem from familial relationships.
You admit it's strange she wasn't included in the group chat but think it doesn't matter because everyone knows you will invite her anyway. To her, it would feel like more rejection and more exclusion. Just more 'proof' that she isn't liked, doesn't have any friends and is being 'tolerated' for your sake.
This will make her feel shit about herself.
As a result, she may quietly think you'd be better off with someone else, wonders why you aren't with someone that other people like, maybe you don't actually 'like' her either?
If there is family stuff to explain it, she might feel guilty or ashamed and she might feel bad for you that you are with someome that other people don't like; someone who not even your mutual friends wants to actively include.
Things are good when it's just the two of you because thats safe but other people might feel 'risky' to her. That doesn't make it healthy or right but if that's how she feels, it won't be something she can just logic herself out of.
When you get angry, it will just reinforce this negative spiral of thinking.
Like I say, I'm not saying that the above is true of her - I don't know her! My point was that these patterns of thinking are often very complex and make perfect sense to the person experiencing it.
And tbh, I'd agree with her that these people don't much, or actively like, her. It is strange to set up a group event and include everyone but one person on the assumption someone else will invite her anyway if they are supposed to be mutual friends - it would be normal if they'd never met her or barely knew her. It has sent a clear message to her that they don't actively want her there. And that is what she has heard.
She's also been/being excluded from any of the chat or planning around it and we all know that that is where the fun starts. Instead, she's just being expected to turn up on the day already on the back foot and when she already feels bad about herself.