How is pollution a market failure?

A few production factors (with the corresponding profit shown in blue)

For instance, let's say I want to produce a chemical that could save lives; I need a place to do so, so I pay to hire a place. Next, I want a machine to produce a lot of it, so I buy a machine and pay for it. Since I can't do it all by myself, I will hire workers to assist me. Now that I am making money from the chemical, I can sort of pay for the company that I just started.

Since air is not for sale, I am not required to pay for the pollution caused by this process, and I will not compensate the surrounding community for the adverse effects of my business because I am unsure of the appropriate amount to pay them. After all, what is the value of air?

This oversimplified scenario demonstrates how we think of pollution as something that doesn't cost money. It can occur when you use natural resources (trees, rocks, and oil), in addition to when you make chemicals.

In this case, I don't think too far ahead about what this pollution could do to the environment because it's difficult to predict what will happen. Perhaps when producing at this rate, there will be an issue in 50 years.

Now that the government is involved, how can these pollution issues be addressed? Since pollution is a problem that affects the entire population, the government will enact laws to correct this market failure. Some examples of these laws include limiting the annual pollution output of factories or imposing other restrictions.

Just to be clear, I'm not an expert on this topic, so this response is probably incomplete and/or rife with errors, but it should still provide you with some information regarding your query.

Pollution is considered a market failure because it results from the inability of markets to allocate resources efficiently. In a market economy, firms and individuals are not required to pay for the negative externalities they impose on society through pollution. This leads to an overproduction of goods and services that generate pollution, as firms do not bear the full cost of their actions. As a result, the market fails to account for the social costs of pollution, leading to an inefficient allocation of resources and negative impacts on public health, the environment, and overall well-being.