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Infertility - most people with KS are infertile plus the treatment (testosterone) kills any chance of extracting sperm capable of reproduction;
Apathy - this can be extremely debilitating as apathy of the type related to KS is defined as borderline "severe depression";
Gynecomastia - this can be quite pronounced - even in pubescent boys for which teasing and bullying can become a real problem;
Children with KS and even adults in later life can have difficulty reading, writing and speech. Social skills tend to be lacking as KS people are shyer, anxious, less mature than their peers. They also have poor judgement, do not handle stress well, suffer with anxiety, depression, paranoia.
Teeth loss - most KS sufferers lose all their natural teeth at an early age. The only options available are dentures (which in themselves can cause issues) and implants (but only if the bone is hard enough to take implants (2+ years of testosterone and a high T level is required).
If there is just one thing that could be removed with KS it would be the lack of fertility. So many marriages have failed due to the partner, wife, lover finding out that their male partner / husband is infertile.