Fingerpicking styles and technique..?

My last two guitar instructors have attempted to show me songs that require finger picking, but were surprised when I did not copy their use of only the thumb and index finger. I taught myself how to finger pick, using all five fingers on the strumming hand. Many tutorials on YouTube also use just the two fingers. Why do most do it this way, while others like myself are more comfortable with using all five fingers? Also, what are the names for both of these styles?