this is the sequence of events as i understood from your post:
1. you met a guy
2. he showed interest and invited you to meet his family; his family invited you to an OOS trip.
3. you freaked out a bit but decided you wanted to keep him as a friend
4. days after your birthday, silence/inactivity, prompting you to call and text him.
5. when he didn't budge, you poured your heart out to his sister
6. you called/texted him incessantly
7. when you finally got hold of him, his brother ended up having to break up with you (as most casual non-relationships go)
that sounds like a whole lot of trouble for a "friend".
i know it's upsetting but that's dating. you win some, you lose some. initially, there's a lot of energy but people lose interest over time. and while you were expecting that he'll woo you until you cave, that's not how it works. you're not being courted-you're trying each other out. it doesn't mean you're not worthy of being loved and all that melodrama, it just means you don't belong together.
i'm guessing that he already decided some time prior to his attempt to cut ties with you, that he wanted to end things with you. but your running to his sister and don't be offended-your constant attempts to get in touch with him that to me sounded really desperate-probably ticked him off.
regardless, he and his brother acted like annoying, little kids. that was just not cool, what they did to you. but in the end, at least you have your answer- this guy never was the one. so there's no reason to cry over him or even spend time thinking how things could've been different.
next time you meet a guy, don't assume anything, don't be easily impressed. dating/hanging out means you both can walk away any minute. there are no guarantees. you cut your losses and move on and you wait for that someone who'll stick.