why? is this just a computer science problem , or is this a mathematical property.
I'm not sure what level of answer you're looking for, so (at the risk of appearing stupid) here's my explanation:
0 is nothing. A negative number is the absence of something, a deficit. Subtraction is the removal of one quantity from another quantity. Therefore subtracting something from nothing results in a deficit, and absence, a negative number.
If I want to make 3 a negative number, I can subtract 3 from 0.
As a bonus, you can also make a number negative by multiplying it by -1.