Can charge really not be created?

if I take out some electrons from a neutral body, it would become positively charged. So didn't I just create some charge

You didn't create anything.

The electrons were already there (and so were the protons that make up the positive charge).

All you did was move them.

When you talk about conservation laws you have to include the whole system. If you're removing something from something else, you and what you remove are all part of the system to be considered.

EDIT :

A comment by @luk32 suggests mentioning a situation which can arise in particle physics where e.g. a neutral particle can decay into charged particles. Note that we again consider the complete system and when we include the new charged particles we find that they have a net charge of zero.

Many more complex conversions are possible in the quantum world, but again electric charge must be conserved and we have to pay careful attention to the what is include in the complete system to balance our sums.

An example of such an event might be the decay of the neutron.

According to this formulation of the principle, you have just considered a system which is not isolated at all. Indeed a physical system is said isolated if it can exchange neither matter nor energy with the rest of the "universe".

Taking out some electrons from a volume of matter is equivalent to an interaction between two different systems: the one which is drawing negative charge and the other which is losing it. The right way of applying the charge conservation is to consider the (isolated) system made by the union of the previous two, which actually conserves a net zero charge.

Taking out electrons from a neutral body is analogous to saying $$0=1-1$$
You can write $0$ as the sum of $1$ and $-1$ but the $0$ doesn't go anywhere, it is still there. If you took some $-q$ charge out from the body, you also left behind $q$ charge on the body. So the net charge is still $0$.