You brewed it too hot. If you brew it too hot, it will become bitter. This is probably the most common of all mistakes, and one which has the most influence over the taste. Depending of the variety of green tea, it should be brewed around 175 degrees F, give or take 5 degrees.

You started off with old green tea. Green tea, "when properly packaged", has a shelf life of about 6 months. Once opened, you have about 2-3 months to use it. That's for properly packaged (vacuum packed or nitrogen packaged) tea - If your green tea wasn't packaged properly and is exposed to any amount of air, it probably was never good to begin with.

Your green tea was from a late harvest. It's no big secret - the best green tea comes from the first harvest in late April, early May. You can get this throughout the year, however.

You brewed it too long. This depends on the variety, but generally speaking, no more than 2 minutes.

You used too much tea. This is where you have more room for adjustment. Again, it depends on the variety, but for normal sencha, about one teaspoon to 8-10 ounces of water. For one type of tea, you may have to use an even level teaspoon, and for another a heaping teaspoon