I think it’s important to make sure you are brewing it correctly. Green tea is even more finicky than black tea, and can get bitter in a hurry.
First of all: Don’t make it with boiling water. Very hot – 175 F, 80 C is as hot as it should be. Use about 4 grams of loose leaf tea per 100 ml of water (or 4 ounce teacup). Then, only steep for 1–2 minutes.
You can use the same leaves two or three more times.
Good green tea is an acquired taste. You can start off with a touch of honey, but I think after a few goes, you’ll drop it and enjoy the tea for what it is.