Question

why it is dangerous to leave plastic bags near a burning gas stove

Answer 1

Near the burning gas stove, there is heat in the air.  Due to the radiation of heat, the thin plastic polymer can get heated up and melt easily.  Due to this there will be holes in the bag.  If there is any thing in the bag, it will get spoilt or polluted.

Also the vapour of plastic bags produce toxic gases.  It is not good for health.