Y chromosome does not equal male. In most cases it does but you can't make a blanket assumption that sex is entirely determined by chromosomes because it is not.
Addressing only this part: "Chromosomes are directly responsible for most developmental differences between living creatures."
Chromosomes are only part of sex differentiation in utero. Many of the developing embryo's/fetus' sex characteristics, both neurological and physiological, are the result of how it responds to the particular mix of hormones it is exposed to at different developmental stages. Sometimes the levels of androgens and estrogens are not consistent throughout the entire development process so the baby can be born with neurological characteristics of one sex but physiological characteristics of the other.