You will find plenty of people that do no accept the US inflation numbers, if I understood it correctly, because it excludes mid-class expenses like housing and education.
CPI includes both housing and education. If there's any argument to make it is around how they are calculated and the degree to which they are weighted in various inflation calculations.
CPI doesn't include food or energy, I believe.
Use the GDP deflator as your measure of inflation to get around those issues.
You still have to worry about hedonic adjustments, though.