Gas stoves, or gas flames of any application, do not cause asthma. No basis in science or even in speculation. The flame DOES produce water vapor, two units to each unit of carbon dioxide.
Carbon dioxide does not cause asthma. Neither does water vapor. Both are essential to life.
Of the two, waster vapor is a MUCH more powerful “greenhouse gas” than carbon dioxide, simply because the water molecule has a “triple point” between solid, liquid, and gaseous states under normal atmospheric pressure and temperature conditions, while carbon dioxide does not. And there is WAY more water vapor in the atmosphere than carbon dioxide.
I remember in univ bio class there was a definite thing with roaches and asthma. That seemed to be a thing to looked at.