This is a very basic law of nature. It is not really possible to answer why!
That's metaphysics to explore questions like this.
Like if you ask me why do like charges repel and unlike charges attract, that would be a similar question.
If you however ask to measure the force between two charges you'll succeed and be satisfied.
That's how it is.
Coming back to the magnetic force, it magnetic force on a charged particle is given by the Lorentz force law as,
However, Lorentz force law is no explanation to why such a property is encountered.
The law is formulated according to the basic rules of nature. It's a Mathematical representation of the fact that the force and the particle's velocity are perpendicular.