Why are metals ductile instead of brittle?
Because the delocalised electrons are free to move.
Metallic bonds are formed by the electrostatic attraction between the positively charged metal ions, which form regular layers, and the negatively charged delocalised electrons. These are the electrons which used to be in the outer shell of the metal atoms. These delocalised electrons are free to move throughout the giant metallic lattice, so as one layer of metal ions slides over another, the electrons can move too keeping the whole structure bonded together.
This is the opposite of what happens in a giant ionic lattice, where both the positive ions and the negative ions are locked in place. If the crystal is stressed and one layer moves with respect to another, the positive ions can end up lined up with each other, and the negative ions lined up with each other. This causes repulsion, so the crystal fractures.