Why can't any number be divided by zero(0)?


The mathematicians will tell you that it is really inconvenient to allow division by zero in most algebraic systems, so it is  decide that it is undefined. 
Imagine dividing $a$ by $b$, i.e $\frac{a}{b}$, is asking you to split $a$ into $b$ equal parts. This can be viewed as, if $a=0$ means you have nothing, and you are required to share zero among few people, it is perfectly sensible to split into as many parts as you like and share your nothing with $2$ friends, $3$ friends, $nth$ friends. Every friend gets nothing. So $\frac{0}{b}=0$, for integers $x$ that are $1$ or larger. Or, $0=b(0)=0$.
But in the case where you are dividing something say $a$ by zero, it means finding how many zeros will make up $a$. There is no sensible number of zeros that will make up a nonzero $a$. There is no $x$ such that $a=x(0)$, where $a$ is non-zero. You could invent an answer and give it a name (infinite), but this new thing would have to fit in nicely with all the other arithmetic you know how to do. 

Also, non-zero numbers on the Riemann Sphere can be divided by zero. There are lots of good continuity properties for arithmetic operators on the Riemann Sphere but $\frac{0}{0}$, $\frac{\infty}{\infty}$ and $0\times{\infty}$ are undefined and  $a+c=b+c$  no longer implies $a=b$.
On the other hand, if you want the usual arithmetic properties associated with a Field, then you cannot divide by zero because zero cannot have a multiplicative inverse and, in a Field, division is defined by:
$a÷b≡a×b′$  where $b′$ is the multiplicative inverse of $b$.
So there is a choice between having the arithmetic properties of Fields and being able to divide by zero but you cannot have both, and we usually prefer the usual arithmetic.