Learning synths...

I just started keyboard lessons and i'm wondering if playing chords with your left hand is the right way. My teacher says it's the only way but i see a lot of keyboard players play two handed...

Almost every teacher (myself included), when teaching pop styles, will start a new keyboard student out playing harmony (chords) in the left hand, and melody in the right hand. This simply seems to be the best way for students to develop independence at an early stage, while also allowing for reasonably quick musical progression. Basic harmony can then progress to rhythmic harmony, and melody and harmony can then be integrated in both hands and all voicings.

I have to say that the question "What should I do with my left hand" is probably the most universal question I've heard keyboard players ask. I should know - I'ved asked it myself. There isn't one right answer. Chords are OK sometimes, here are some other thoughts:
1. Single note - works if you are playing a sustained sound like a string or pad. Works especially well if the chord progression uses that note as a common note. Helps avoid clutter.
Example: C - F - G - F - C
Left Hand: a low C
Right Hand: C-E-G / C-F-A / D-G-B / C-F-A / C-E-G
You could also help eliminate more clutter by leaving out the middle notes in the right hand chords. Lots of variations...
2. Octaves - boy, that one carried me for a long time! Better suited with piano sounds (think "Jerry Lee Lewis" and sixteenth notes). Melody on top, root of chord played in octaves below.
Example: C - F - G - F - C
Left Hand: a low C + another one an octave up
Right Hand: C-E-G / C-F-A / D-G-B / C-F-A / C-E-G
3. Fifths - same concept as above, just play a C - G in left hand.
You can experiment with other left hand options like sevenths, major sevenths, play the third or fifth instead of the root, etc. My advice - start small, master that, play around with cool sounding stuff, then pick a new target and repeat.
I hope some others have some other good ideas that I can pick up... :D