I do have proper ventilation, but "proper" ventilation – short of a laboratory setup – doesn't exist for piping methane (95% of what "natural gas" is along with carcinogens like benzene) directly into your kitchen and then combusting it to produce nitrogen dioxide. You should not be using a gas stove if you care about your respiratory health or the respiratory health of your family.

Edit: this user is literally just making shit up at this point. Below, they cite this article as evidence that fans adequately reduce PM2.5 and NO2 emissions. Let's break down what this article is actually about, because I believe they expect other users not to read it knowing or simply not caring that it doesn't do that whatsoever. This article is about if running the fan after cooking helps reduce harmful indoor pollutants. As you can see from the abstract, it makes no assessment as what "adequate" would be, but we can continue into the article itself, which immediately reads as follows (I emphasize that I've read the entire article, and at no point do they claim that the pollutant levels even when following best practices are acceptable for human health):

Cooking is a significant source of indoor pollutants. High emissions of particles from cooking activities have been reported in many studies [1–9]. Kearney et al. [5] found that about two-thirds of the 100 Canadian homes studied had higher contributions of ultrafine particles (UFPs) from indoor sources (mainly cooking) than from the entry of outdoor UFPs. Wallace et al. [10] found that cooking was associated with an increase of a factor of ten in the concentration of UFPs and an increase of a factor of three in fine PM 2.5 . Wheelet et al. [8] reported that during the dinnertime cooking period, indoor UFP and PM 2.5 concentrations exceeded their daily mean values by, on average, 160% and 60%, respectively.

For homes with natural gas cooking stoves, higher residential levels of nitrogen dioxide (NO 2) are an additional concern [11,12]. A recent simulation study [13] found that gas burner use may routinely lead to NO 2 concentrations that exceed the 1 h U.S. ambient air quality standard of 100 ppb and follow-up measurements found that the threshold was exceeded by moderate burner use in four of nine homes in which experiments were conducted [14].

Many studies, both experimental and simulation, have demonstrated that kitchen exhaust fans can reduce cooking-related air pollutants [14–21]. However, the efficiency of exhaust fans to capture cooking-related pollutants can vary widely based on a number of factors, including equipment type, size and location, exhaust flow rate, exhaust ducting, installation details and use behavior [15,19,22,23].

Use behavior is an important factor to maximize effectiveness, especially for those who are not able to purchase a higher performance unit or make improvements to the installations, such as renters.