What does the phrase no wife no horse no mustache mean?

It was a standard that West Point enforced. No Horse restricted the ability to travel, No Wife meant your time and allegiance wasn't split and No Mustache was a statement that you were not independent.

I question any High School boy with a mustache as it indicates he thinks himself a man. Only one man is allowed in a home, and that is the patriarch. Growing a mustache means it's time to leave the nest.