Daggers can do either slashing or piercing damage, and have a range increment of 10'. I don't see anything in the rules to suggest that thrown they only deal piercing damage...though it seems like a reasonable rule.
Am I missing something?
Yes - It's Attacker's Choice
The dagger weapon entry says "P or S" for its damage type, as you mentioned. The important part is how you resolve the two types, which is here (emphasis mine):
Some weapons deal damage of multiple types. If a weapon causes two types of damage, the type it deals is not half one type and half another; all damage caused is of both types. Therefore, a creature would have to be immune to both types of damage to ignore any of the damage caused by such a weapon. In other cases, a weapon can deal either of two types of damage. In a situation where the damage type is significant, the wielder can choose which type of damage to deal with such a weapon.
You always get to choose which one you want, even when throwing it.
If you wanted to houserule it that it only does one type when throwing it, you certainly could. But it's not a core rule.
The rules let you do slashing damage with a thrown dagger, and that's physically reasonable when spinning it.
According to the laws of physics, you get a large contribution to the kinetic energy of an object by spinning it - especially if the object is heavy and weghted in the correct way.
The linear momentum is one thing (ie: p = m × v), but by spinning you also get angular momentum: L = r × m × v
A thrown dagger will only deal straight piercing damage if you land a hit without spinning it. Otherwise it will be a linear combination. Imagine a spinning dagger, just as it is about to hit its target - it will be a slashing motion combined with forward momentum.
The faster you spin the dagger the more slashing damage you will do.