There are a couple of reasons for this. The first is out of concern for the environment.

Much of the plastics, magazines or other garbage have been manufactured using toxic chemicals. The burning of these materials releases these toxic chemicals into the environment, sometimes in an even more dangerous form than before.

I strictly discourage the burning of garbage, especially in your masonry heater. Besides releasing toxic chemicals into the environment, the burning of plastics and garbage can prematurely damage your heater.

These things do not burn as cleanly as dry wood and can leave very messy deposits on the inside of the heater.

It is just a better idea all around to stay away from burning garbage, especially in a masonry heater.