In his blog post, *Could Nature, LHC, prefer \(\mathcal{N}=2\)* *supersymmetry?*, @LubošMotl remarks that:

Before the experts leave this article with the word "obvious bullshit", let me say that they only talk about the extended supersymmetry of the gauge sector. It would really lead to contradictions if you tried to extend the quarks and leptons to N=2 multiplets.

What exactly are the anomalies that arise when we extend gravitons and fermionic particles to \(\mathcal{N}=2\) (32 supercharges)?

Also, how is it possible to have a different number of supercharges for different sectors?