Eileithyia is the goddess of childbirth, and the reason why is most probably because of Leto fleeing from Mount Olympus because of Hera's demands, leaving her nowhere to go when she wanted to give birth to Artemis, the goddess of the moon, and the hunt, and Apollo, the god of the sun and truth. Leto luckily found an island, ruled by Eileithyia. She also is related to Hera, and Hera might not have known that she let Leto on her island, the island of Delos. It was a rather hostile and desolate island and no one really goes on it. Still, Hera sent Iris to abduct her in order for Leto refrain from giving birth.
Despite Hera being the original goddess of childbirth, she is a helpful goddess that looks aggressive and dangerous, though is willing to lend a helping hand to anyone that is in need of her assistance.