It's because the reproductive strategy of humans (and many other animals) involves the mating of two sexes, with each sex providing a distinct type of gamete: eggs from females, and sperm from males. There's no third type of gamete and therefore no third sex.

The chromosomal abnormalities mentioned earlier don't define new sexes, but rather, phenotypic variations within the two sex categories. For example, people with XXY sex chromosomes develop as male, but with smaller-than-usual testicles that either underproduce sperm, or can't produce sperm. They also tend to be taller and have less muscle mass.

Another example: people with XXX sex chromosomes develop as female, generally with normal sexual development, including the capacity to get pregnant. They also are usually taller than average, and have a higher risk of learning disabilities and developmental delays.

This is all described much more extensively in the literature. Any general biology or developmental biology textbook should be good for providing further details.