That's not true. There are many scenarios how one can live legally in the US for more than 6 years as a non-immigrant. E.g F-1 student visa for 4+2+4 years (Bachelors through PhD), followed by 3 years on OPT, followed by 6 years on H-1B. That's 19 years.
Ya. You can only be in a H1B for 6 years, but combined with an F1 and OPT, could be longer. I was just thinking about working visas.
You have to get a green card after your second work visa or go back home, that's the choice. Unlike other countries where you can work on a working visa indefinitely and never even qualify for permanent residency.
In addition, nobody "makes" you get a green card.