When regarding the CPI, why is the selection of G&S within it always favorable to what it has been for years? I ask because some economists and businessmen have seemed to find goods and services that have proved the CPI and inflation cohesion wrong. Are they fishing to deeply to find G&S that is to abstract? Or is that they are opening a larger topic of discussion that no one wants to believe?
Price measurement in most national and international agencies is based on the “statistical approach” to price indexes developed by Dutot (1738), Carli (1764), and Jevons (1865). The methodologies developed in these papers form the foundation of 98% of all consumer price indexes generated by government statistical agencies (Stoevska, 2008). Following this approach, statistical agencies are more likely to select a good for inclusion in the sample with a past high sales share. Because agencies typically choose products based on their historic sales shares, this explains why "the selection of G&S within the CPI is always favorable to what it has been for years".
Economic theory has largely rejected the "statistical approach" to price measurement in favor of the "economic approach," which asserts that all price indexes should be derived from consumer theory and correspond to the unit expenditure function. See Redding and Weinstein's paper "A Unified Approach to Estimating Demand and Welfare", they provide the argument and the above references.
Is CPI accurate relative to... what? If you are asking whether CPI is accurate as a measure of the true cost of living, the answer is no. One reason for this is that the CPI is computed using a weighted Laspeyres index of prices of different goods and services, weighted by their share in consumption. Prices are continually updated but weights are not, and hence the headline CPI index neglects substitution effects. Let me present a highly simplified example; two goods in the economy, apples and oranges, both consumed equally (weights 0.5 / 0.5). At the start, the price index computed using CPI methodology will be 100. Now the price of apples rises 10% and the price of oranges stays the same. As a result, people substitute out of apples and into oranges - so apples' share of consumption falls from 50% to 25%. The consumer price index would now stand at 105, implying a 5% increase in the cost of living. However, the true increase in the cost of living is 2.5% - CPI has overstated inflation in the cost of living through failing to take account of substitution.
Most countries reset their CPI weights yearly. Some, e.g. Japan I believe, reset once every decade only. Obviously the less frequently you reset your weights, the worse CPI will be as an accurate measure of the cost of living.