I'm not concerned or uncomfortable with the message itself; my concern is that the message goes exclusively to its intended audience. An email or text message can sit around and eventually be viewed on accident or by someone nosy. At least with Snapchat, I have a level of assurance that this possibility is minimized.
Hell, most of us do it in real life. I say plenty of things I wouldn't necessarily want provided to my mother or employer, and small audio recording devices are cheap. I trust my friends and partners to not save and share unflattering snaps the exact same way I trust them to not record our real life conversations.
If you're planning to run for President some time in the future, maybe it's worth it to always act as if the public is watching. I think the rest of us are fine.
I'd argue it's stupid that we archive and collect every meaningless conversation we have.
Another way of phrasing that argument is that if you look through my snapchat screenshot folder vs the received images from my SO, the snapchat screenshot has a higher density of content worth keeping.
Between my SO and I, for stuff that's more memorable and may want to be saved, we'll use email, but for stuff like "look at this weird sign I saw downtown", we'll use Snapchat. An app is all about its use cases.
I'll grant you the feature of drawing on pictures though.