Question

why metals are ductile instead of brittle?

Answer 1

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.

Answer 2

The sliding of atoms when force is applied is the reason that metals can change their shapes. Since all things are made of atoms, including metal, the atoms must be moved in order to change the shape of the metal. Whether a metal is malleable, ductile or both, most metals are able to be changed with the use of force because their atoms are movable. In most, if not all metals, it is easier for the atoms to move when they are heated which is the reason that most metals are melted down or heated up before they are moved into a different shape.
Most metals are both malleable and ductile, but malleable and ductile are two different things. Ductile metals are able to be pounded down into a smaller, thinner sheet of metal. Malleable metals, like copper and nickel, are able to be stretched out into thin wires. Copper, nickel and tin are a few metals that are able to be pounded into thin sheets and able to be made into thin wires. When atoms move in different ways and can be pounded or stretched, they are both malleable and ductile.