Why minus multiply by minus equal to plus?

Let's use the number -5, and look at the simple multiplication table:

-5 x 2 = -10

-5 x 1 = -5

-5 x 0 = 0

As you can see, the numbers on the right are being increased by 5 every time. So

-5 x -1 is 5

Another helpful way to think of it is common sense.

If I say to you, "Eat," I am telling you to do something (+)

And if I say "Do not eat," I am telling you to do the opposite (-)

But if I say "Do NOT not eat," I am telling you not to starve, and therefore to eat (+)