The synthetic reed question, in fact the whole "what's the best reed with this mouthpiece" question doesn't have an answer. It's like asking "what's the best color." You answer and I say "wrong." Doesn't shed much light on the issue.
I've got a Grabner "Legere friendly" clarinet mouthpiece. I play Legere on it and like it. I have Legere tenor and alto sax reeds in several strengths that I try everytime I get a new mp and then I put them back in the drawer. I have Fibracells that I've used almost everyday for two years. On some mps they can sound a little buzzy. On other mps, they are perfect. I have a Hartman carbon fibre that sounds like a model airplane engine on a Rico Metalite but sounds almost sedate on my vintage Buescher hard rubber. It is so dependent on the mouthpiece, and probably just as much the player, that generalizations about synthetics aren't of much value.
Which leads me to the two most common generalizations. First, the generalization that synthetics are bad. Sort of like saying sex is bad. Chances are the speaker just hasn't experienced it in the right way, in the right setting, with sufficient practice, whatever. The more accurate statement would be "it's not for me" or "I don't enjoy it," or "I'm not that kind of person" and leave it at that.
The second common generalization seems to be that they are practical, i.e., they are "plug and play," don't require breaking in, are more consistent and cost effective. That's been my experience. I use them when I practice at home because I can walk into the room, start (then the phone rings), start again (doorbell), start again (then lunch), etc. This same benefit applies to lessons. During a 45 minute or one hour lesson, do you really want to spend the first 10 minutes compensating for a cane reed warming up?
Tell your teacher that you'll switch to cane if the lessons are discounted by 20%.