Why do my 0.5 mm pencil leads shatter?
It's unusual for the problem to be the pencil unless it's been damaged, like by dropping it on the tip.  The most common issues are remnants of old leads being pushed out by the new lead, a jam, or defective leads.
Start by releasing and dumping all of the leads and lightly tapping the back end of the pencil on a hard surface to encourage any lead fragments to fall out.
I'm not sure about rOtring, but many 0.5 mm pencils come with a cleaning wire (often stuck into the backside of the eraser).  If it didn't come with one, find a thin straight pin or piece of stiff wire thin enough to fit into the tip.  While depressing the feed actuator all the way to open the feeding collet, slide the cleaning wire through the tip to dislodge any lead remnants that might be stuck, inserting it far enough to go all the way through the tip and feed mechanism.
If you don't have anything to use as a cleaning wire, disassemble the pencil all the way to the feed components.  Inspect everything to ensure there aren't lead bits stuck in anything, or lead dust packed somewhere.  Then reassemble it.
Take a good lead and carefully insert it through the tip while fully depressing the feed button to open the feed mechanism.  Push the lead all the way in so only a normal amount of lead is exposed, then release the feed button.  Work the feed button a few times to verify that the lead feeds without breaking.
If it works, you're done and can load in some extra leads.  Don't overload the pencil with too many extra leads, though.  The spare leads need room to move in order to load when you finish the previous one.
If the lead breaks when you try feeding it, try again loading a harder lead.  If that feeds without breaking, the problem is the leads.  It could be a bad batch.  If the hard lead also breaks, that would point to the pencil being damaged.