Green LED: Forward Voltage
There's green and then there's other green.  This is why in engineering we use numbers instead of vague words.  It is best to specify the actual wavelength.

Most common "green" LEDs are on the yellow end of what most people consider green.  These do have about 2.1 V drop at reasonable currents.  This type is the cheap and common "green" variety.  This wavelength of green corresponds well to the peak sensitivity of our eyes.

There are other "green" LEDs that use different semiconductor substances and are more toward the bluish end of what most people would call green.  These of course have a higher forward drop due to the physics you seem to understand correctly.  These are much less common and typically more expensive.  Their lumen specs also don't look as good, in part because this wavelength is a bit shorter than the peak sensitivity of human eyes.

My guess is that your professor deliberately gave you the unusual green type of LED to make you think a bit, learn not to take things for granted, and impress on you the need for real numbers as opposed to vague words like "green".