How can declining diversity cause extinctions?

This is because if we strictly only allow people or things of our type to mingle, there are not enough of us to keep the population going, because then reproducing would be slower and we'd die out, and it would happen that some people who insist on finding "soulmates" that are perfect for them wouldn't find it in their group and refuse to reproduce, therefore making the population even lower.

What is your question then