Why it is detrimental to the environment and humans if battries are not disposed of in a responsible way?

Batteries sometimes contain heavy metals, Mercury being the most problematic. These can get into soil and water and from there, they can get into plants and animals.

If you eat an animal or plant containing heavy metals in their body, those will pass onto you. So it's bad for the whole food chain, humans included.

There are many documented health effects due to heavy metals.