Actually, you are reading it wrong. Aasimar are native outsiders, not outsiders.
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What you are reading is the template applied to a base class. In this case a paladin character. Go by the template, not by the write up.
So here is what you get when you have an Aasimar character:
— +2 Wisdom, +2 Charisma.
—Medium size.
—An aasimar’s base land speed is 30 feet.
—Darkvision: Aasimars can see in the dark up to 60 feet.
—Racial Skills: Aasimars have a +2 racial bonus on Spot and Listen checks.
—Racial Feats: An aasimar gains feats according to its class levels.
—Special Attacks (see above): Daylight.
—Special Qualities (see above): Resistance to acid 5, cold 5, and electricity 5.
—Automatic Languages: Common, Celestial. Bonus Languages: Draconic, Dwarven, Elven, Gnome, Halfling,
Sylvan.
—Favored Class: Paladin.
—Level adjustment +1.
Native subtype:
A subtype applied only to outsiders. These creatures have mortal ancestors or a strong connection to the Material Plane and can be raised, reincarnated or ressurected just as any other living creature. Creatures with this subtype are native to the Material Plane (hence the subtypes name)
Unlike true outsiders, native outsiders need to eat, sleep and breathe.
Aasimars, tieflings and other plane-touched creatures are not true outsiders. So they don't get outsider abilities like weapon proficiencies. They have to get them through the classes they take. Hence, the reason why they are a playable race. And a very fun playable race at that.
