"As the good guy, Kal-El can stop Zod and the rest of the bad aliens. Unfortunately the ones from the black ship are all bad." April doesn't want Lana to think all Kryptonians are necessarily evil. Or things for that matter.

April knows that blood would help her heal faster, but she can't ask (or take) for any in front of Lana. "We should get Lana to safety."