Why are metallic bonds non directional?
When we think of the type of bondings in metals, we should take into consideration the difficulty in separating metallic atoms from each other (metals are hard materials), with the possibility of moving them around ( malleability and ductility ). Moreover, the conductivity of electricity and heat in all directions.
Taking all these facts into consideration, the bonds in metals have to be strong and nondirectional.
A simple picture that can explain bonding in metals is the electron sea model that suggests that the atoms are positively charged (cations) swimming in a sea of electrons (Figure below):
Image source: Zumdahl textbook .
In other words, bonds in metals are nondirectional because the electrons are NOT shared with one atom in one direction; however, they are shared with many other neighbouring atoms in all directions.