Why are igloos made of ice, aren't they supposed to keep warm?

Igloos are supposed to protect from the outside temperature and wind. I will be happy to critique your thinking.

Igloos are made of ice in regions where no other building materials are available. They are much better than no shelter at all. They reflect the radiant heat from bodies inside, and as BobPursley's has stated, they protect from wind and lower temperatures outside.

Because the ice acts as an insulator. The water will freeze to a certain point and will be near freezing, but the ice above will allow the water below to maintain it's heat energy.