A green card is NOT a visa my friend. Getting a green card is a very involved process.

So why would you need to leave the country, if you couldn't figure out why you don't want to issue one in the year+ it takes to jump through the hoops

Just a fun fact, getting a green card means signing up for ten YEARS of tax liabilities in the US. And those 10 years start, AFTER you relinquished it...