Snapchat is a tool that primarily allows a user to become closer to (1) acquaintances, and (2) existing friends who may have drifted away over time. Let's rephrase this a few ways to unveil the value. Snapchat is a communication tool that's useful for overcoming shyness. Snapchat allows users to break the ice, facilitate conversation, and overcome awkwardness. Snapchat allows the user to converse with acquaintances and distant friends that would otherwise be too awkward via other methods like texting, email, Facebook, etc.
In fewer words, Snapchat makes communication trivial.
Just Snap a picture of something, add some silly text or a drawing on top, and push it out to everyone. After all, what's the harm? The picture goes away, and if no one Snaps back it doesn't really matter. There's no evidence of a failed attempted communication, e.g., an un-responded email, text without a reply, comment on a wall without a Like or a response. In this way, Snapchatting is a lot like fishing. Cast your snaps, see which old friends or acquaintances reply, and strike a conversation, hang out, hookup, etc. later on.
The disposable aspect of Snapchat provides a new medium for conversation starting. You know what conversation leads to? Deeper friendships. And who's really interested in knowing who your friends are? If you aren't making "new friends" on Facebook, but elsewhere, you can see why Facebook might be startled. But that fear starts to compound when you consider aging relationships are being nurtured on Snapchat as well.
After all, if you aren't reconnecting with your current friends on Facebook, what good is it? All that's left is the News Feed and what everyone is up to. Hm. Enter Snapchat's "My Story" feature, where you can essentially create a 24-hour lasting Snap, very similar to status updates on Facebook. Interesting.
I'm not sure Facebook being cool or uncool has much to do with it. I suggest the bigger factor is being able to communicate with peers, despite shyness. Overcoming awkwardness, facilitating conversation with a lack of confidence, or whatever you want to call it... Snapchat is a layer below Facebook. Said another way, turning acquaintances into friends (Snapchat) pre-empts the need for maintaining friendships (Facebook).