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The blank (typically just a flat disc) is wider than the finished product and so the metal that will eventually form the wall starts outside the perimeter of the finished product. When the punch moves downwards, it hits what will become the bottom and then "draws in" the rest of the material. Hence the name.

See https://www.manufacturingguide.com/en/deep-drawing for a graphical illustration.

Blacksmiths draw out metal by pushing with their hammers. Same thing.

It's only pushing from the perspective of the punch.