Some good replies from PP. Just wanted to add that there is no such thing as a typical person or standard formula when it comes to alcoholism. It can happen to anyone and can be driven by any number of things - boredom can be just as bad as stress - and there is a strong genetic component in many cases, so it happens even if there’s no big underlying “trauma.”
For your cousin, who knows. Maybe she’s been drinking in secret a long time, maybe she struggled before and was trying hard to be sober for a while but then relapsed, maybe there was some kind of event or trauma you’re not aware of. Or maybe it just happened slowly and then all at once - for a while it was a glass of wine here and there and then all of a sudden it was out of control.
To me it’s clear you’re coming from a place of curiosity rather than judgment, but I would just be hyper-aware of the language you use around her. People are very fragile in early sobriety and are told to avoid any “people, places, or things” that might trigger them - even if it’s an innocent and well-intended comment from a relative, it could be tapping into something (a memory, a hidden insecurity, etc.) that makes them want to drink.
I’m guessing this is the reason she wants to avoid family; so she can feel fully recovered and strong enough to interact in a way that doesn’t put her sobriety at risk, even if you’ve done nothing wrong as such.
That said, in rehab there is also a lot of therapy, exploring your family dynamics and past, learning about setting boundaries, etc. etc. While this is really useful and necessary for addicts, it’s sometimes easy to take it too far and to be a bit too harsh on people - especially those close to you - and set up boundaries that aren’t necessarily reflective of your relationship but made from a place of vulnerability + over-therapising.
All the same, it’s probably also not a bad idea to reflect on your relationship with her prior to this and whether you might have said/done something or acted in a way that didn’t make her feel good about herself. Maybe her parents always compared you to her a bit too favourably (through no fault of your own but it still makes her feel a certain way). Maybe you’ve been a bit too judgmental about some aspects of her life in a way you thought was helpful and she perceived as criticism. Only you will know.
Either way, I’d give her some space - maybe just send a supportive message and say you’re there and ready to talk and support her when she needs you (or not talk about it at all and just have some quality time together), and then leave it until she reaches out. The pulling away is probably not permanent, and if it is, there’s probably something underlying it that’s not actually drinking-related, and you’ll have to figure that out in time.
all the best OP x