@Xzayer, Think of travel flasks. Just like homemade-bentou box, it's not unusual in Japan (perhaps in Asia as whole) for students to also bring their own waterbottle from home, usually to not only cut cost on daily pocket money but also to discourage buying and drinking less healthier softdrinks and the likes.
If what confused you is why the little sister even need to borrow the bottle, well i had no idea too.
Thank you. I understand the travel flask. It was the sudden brother I need to borrow a water bottle threw me for a loop. I pictured someone doing that to me still seems strange.
@Xzayer: when I was in school, sharing water containers (water jugs, not just water bottles) wasn't unusual. Not really sanitary now that I think about it, but yeah as mentioned by @Haremmony, it was a way of cost cutting as drinks were extra damage to your already limited lunch money.