Some people have argued that the reported unemployment rate actually understates the extent of unemployment . explain this reasoning and provide 2 examples for support? ?

This is because the unemployment rate give only takes into account people that are unemployed and are looking for work. It does not account for those that are unemployed and have given up.
ex) A woman who looses her job because of technological advances is looking for work and is considered unemployed (taken into account), however a man who has tried looking for work after he was laid off has given up (not counted)
ex) A woman lost her job during the depression and cant seem to get a job with her limited skills. She has given up and is not counted in the unemployment rate