Genetics is not my field. I'm a Bio-Chemist. But still I've read enough recent scientific articles to know that the male gender is not going extinct.
The "expert" that was interviewed in this episode was Jenny Graves. A geneticist who is not taken seriously by her peers. She's never actually contributed anything that has withstood the peer-review system at all. This whole hypothesis of hers is nothing but conjecture with no real evidence behind it. I can't believe that the producers actually thought they should just take her side without consulting the vast majority against the "rotting Y-chromosome"-hypothesis.
Just like another user by the name of IrwinBalaster I urge you to google these headlines: "The y files - Genome British columbia", "Men Not Going Extinct After All - Newser", "Men's Y chromosome is not about to go extinct - NewScientist", "Scientist Says Men Will Go Extinct, Despite Debunking of "Rotting Y Chromosome Theory - counselheal".
Also it's falsely suggested that males are more aggressive than females. Google these headlines as well: "Biology Does Not Make Men More Aggressive Than Women - Culture of peace", "Testosterone Does Not Induce Aggression, Study Shows - ScienceDaily".