What was Ungoliant?

[The Squatter of Amon Rûdh]

I always thought Arachne was turned into a spider in punishment for defying Athena.

That would be too logical. She beats Athena in a weaving competition, which upsets the goddess and Arachne hangs herself in fear. She's turned into a spider to save her life. Greek gods have something of a talent for erratic and bizarre behaviour (see Robert Graves: The Greek Myths).
As for Ungoliant, the punishment idea does make sense. I don't have all of the HoME volumes at home, but I'll have a look and see what I can find...