Why Is There a Discrepancy Between The Length of Time Listed on my B1/B2 Visa and How Long I Was Told I Could Stay For a Visit?

I am visiting my sister here in the United States. My B1/B2 Visa distinctly says that I have five years, but the Inspector at Kennedy Airport only gave me three months. How can I get him to correct this error?
Actually, the visa is only the authorization for the transportation company to take you to the U.S. The five-years written on your visa indicates that within that five-year period, the transportation line may bring you to the shores of the U.S. without any detriment to themselves. The visa does not guarantee your admissibility at the U.S. port-of-entry. The U.S. Customs and Border Protection (CBP) officers are the ones who decide if you will be admitted and for how long, depending on your stated reason for coming here. When you were admitted into the U.S., you were given an I-94 (small white card). On the I-94, the USCIS marked your date of admission and your maximum period of stay, usually a date up to 6 months. You may apply for an extension of that date or you may apply for a change to another visa category.