It is a system that separates people into two groups based on their reproductive configuration, and assigns different values to each group. Males, for example, got money and property, and females got love and home. This rigid separation is designed to force males and females to come together to create a whole life, and in the process to breed. Heterosexism uses firm gender distinctions as a social tool to create a reasonably stable and growing culture, at the cost of individual freedom. This is why, for example, the Roman Catholic church is so heterosexist, so family based, because they want a stable and growing population to expand their influence in the world.
Conservatives speak of family values, while feminists speak of community values.
To erode heterosexism, we need to look at models that don't involve coupling in fixed orbits to determine stability, but rather involve a range of people doing the hard work of culture, which is always going to be to create a stable, loving and powerful place to raise the next generation. The real work of any culture is done by parents, who strive to make the world a better place for their children, for when a culture neglects children, it is doomed to die. This is not about an irrational fear, but about the defense of a system and set of values that people cherish. Heterosexism is the force that lays an entire gender path at the feet of a child after looking at their reproductive organs, and forces some children to have their reproductive organs made normatively appearing at birth. Heterosexism is inherent in the dreams and expectations of the parent that the children will be copies of themselves, continuing thier beliefs into the future.