why does shyvana do so much damage when she has no items

Same reason Garen, Darius, Udry, Olaf, Scarner, Yorick all do damage with no items. They are the same class of champions.

She's a dragon FFS.

She's really easy to deal with - just walk away. Don't stand there and let her eat you.

Because she is a onhit melee champion?

shivana has a free on a ability thats on hit. (minus the extra ad/attack speed/lifesteal/active)