I've noticed some sketchy behavior from Binance. They are now suddenly demanding KYC from me. I've not gone over any limits. When asking the support for an explanation they just offer "out of the box" explanations.
A buddy of mine got the same. We've both been using Binance for over 18 months and then suddenly this happens.
Summary:
DO NOT TRUST THAT BINANCE WILL LET YOU TRADE WITHOUT KYC
Nothing you can do. Just got to submit the docs to them.
With increasing regulation around the world it's pretty much a matter of time before a centralised exchange forcing people to do KYC. Poloniex had to do it, Bittrex had to do it, shapeshift had to do it. And even though Binance let people trade anonymously for quite a while it's apparent that that will come to an end eventually if they were to continue to offer their services worldwide.
That's why I don't store funds on centralised exchanges, it sort of reduces the risks of this happening. Make your deposit, do your trade, and get out right away, unless you are comfortable with providing KYC.