Because your point was wrong. When AZA zoos learned better, they stopped breeding them (and white lions) and now rarely hold them. Outside the AZA, however, they're common and frequently being bred.
My point was not "wrong". If one wants to proclaim that zoos only engage in responsible breeding practices, while private individuals instead opt to throw caution to the wind, than white tigers are a
really bad example to use for that argument.
The first white tiger imported to the US arrived at Smithsonian’s National Zoo on December 5, 1960. Her name was Mohini, she gave birth to her first litter on January 6, 1964. The cubs were sired by Samson, who was Mohini's half-brother... and uncle. Yes, at the same time.
Two of the three cubs produced died of feline distemper just over a year later in August 1965.
Mohini's second litter arrived on February 5, 1966. Samson was also the sire of this litter. One of the two cubs produced was stillborn. The surviving cub, Kesari, was later sent to the Cincinnati Zoo.
Mohini's third litter arrived on April 13, 1969. Unlike her previous two litters, these cubs were sired by Ramana - Mohini's
son, the sole survivor of her first litter. One of the two cubs in this litter died at only two days old due to birth defects. (He starved to death. This cub had shortened tendons in his front legs, this prevented him from being able to knead.)
The surviving cub, Rewati, had crossed eyes, a crooked spine and shortened limbs. She was reportedly sterile, never successfully conceiving.
Mohini's fourth and final litter were born on March 8, 1970. This litter consisted of four cubs... three of which were accidentally killed by Mohini. She crushed them while struggling to give birth to a fifth (stillborn) cub. Ramana was also the sire of this particularly ill-fated litter. The surviving cub was named Moni, he died of a neurological disorder at only 16 months old. He also reportedly had a twisted neck.
Mohini's line survived via her first two children - Ramana and Kesari. They became the proud parents of a litter of four at Cincinnati Zoo on 20th June 1974.
Cincinnati Zoo would go on to become a powerhouse when it came to breeding white tigers.
As over
70 of them were eventually born there.
The AZA only mandated that it's member zoos stop breeding white tigers in
2011. Cincinnati's last white tiger only died in
2018.
White tigers were bred in accredited US zoos for
47 years. Inbreeding was present from the beginning and genetic defects were noticeable from the
third litter bred.