I disagree with the position each of you is taking.
I don't think that there's any way that humans can change sex, no matter what technological interventions are used or how extreme they are. 
But at the same time, I don't agree that it's "dehumanizing" to use extreme (or any other) technological interventions to alter the human body. Nor do I think it's fair or accurate to say "the belief that [some] human bodies are deficient without re-engineering is profoundly anti-human." 
Altering the human body, and believing that some or all human bodies are deficient without some kind of re-engineering, both strike me as as typically human things do do. 
When it comes to sex organs and secondary sex characteristics specifically, the fact is that humans have been using surgeries, substances, prosthetics, cosmetics and other means to remove, damage, enhance or otherwise alter primary sex organs and secondary sex characteristics of members of our own species for thousands of years.
For example, the practice of removing the foreskin of human males aka circumcision has been around for 6,000 years.
The practice of subjecting human females to ritual genital mutilation - by cutting off often large portions of the clitoris and labia, then sewing up the remaining flesh to leave a just tiny opening for urine and menstrual blood to exit through - is thought to have originated in ancient Egypt. Which explains why in some parts of Africa FGM came to be known as "pharaonic circumcision.”
The earliest records of humans intentionally removing the testicles of boys and men to turn them into eunuchs date to Sumeria in the 21st century BC. Over the course of human history, untold millions of boys and men were intentionally castrated by being subjected to procedures to remove their healthy, normal testicles. 
Humans have been castrating animals, particularly male animals, by removing their healthy gonads for thousands of years too.
Very early, it was discovered that castration provided control over sex hormone-induced behavior and breeding in domesticated herd kept for secondary animal products, such as wool and milk. Evidence exists that herd of castrated sheep and goats were maintained during the Uruk period approximately 4,000 BC and some claim as early as 9,000 years ago.
Archeologists have dated [male] castrated cattle in burial sites by examining horn cores and skeletons, in which evidence of hormonal control over growth was observed, long before the field of endocrinology was even established.
The first recorded ... creation of geldings, or castrated male horses, was documented in the 7th Century BC by the Scythians. 
Vaginal hysterectomy - surgical removal of a woman’s uterus through the vagina - dates back to ancient times as well. The first recorded mention of vaginal hysterectomy is in the writings of Soranus of Ephesus, a Greek physician who lived in the 1st/2nd century AD.
But for most of the many thousands of years that humans have engaged in these kinds of practices, no one ever claimed that removing, damaging, enhancing, refashioning or otherwise altering the sex organs or secondary sex characteristics of humans or other animals amounted to changing their sex.
Only in the 20th century did some people (men, actually) in Western countries working in medicine, psychology, sexology, the pharmaceutical industry, and the realm of fantasy start claiming that by altering our bodies in certain ways, humans can undergo “a sex change.”