Why does every matter have a tendency of gravitation (attract objects)?
Gravitation is the tendency for every object with mass to attract every other object with mass.An object exerts Gravitational force due to its mass and it will do that on every other mass in the universe, however, the force decreases with distance. Its quite similar to electric forces which are cause by a particle's charge (rather than mass).
So, everything in this universe exerts gravitational force .