I got caught out by this the other day - my friend asked me why I screenshotted her, when I really hadn't! Embarrassing!
As Kass said, it is usually a glitch with the Snapchat app, and it can usually be resolved by uninstalling and re-installing the app. Apparently, it can be the way you tap on the screen when you view a snap that makes it show that you screenshot - perhaps if you double-tap really quickly without the app registering it properly.
If you think you might have some kind of malware on your phone, it's probably best to get some anti-virus software like AVG Mobile Security which can run scans and remove anything that might be causing you to unknowingly screenshot.
If neither uninstalling nor running anti-virus scans stops Snapchat from telling your friends you're screenshotting, I guess all you can do is apologise and plead your innocence...
You might accidentally fire up the built-in screenshot of your phone through the shortcuts.