Who hatches the eggs of the hoouse finch the male or the female?

The chicks hatch (=gets out of the egg) themselves with a tip of their beaks, "the egg tooth". It will later disappear. They will come out when they have grown too much to be inside the egg. Mother nature will take care of this event, and it's very rare that the parents help the chicks. They know the chicks have to get out themselves in order to live.

If the chick does not get out of the egg, it's weak and too small, and would also loose the battle for food with it's siblings - that's why a chick like this guietly and gently sleeps away soon after it fails to hatch. The parent might also eat it after it's dead to gain protein and other useful nutrients.

It's nature, and mother nature does not do anything that isn't supposed to happen. The chick just wasn't suitable for living.