Hm.. I've never personally seen a clause that says "thou shall not discuss rates with our client", but may have to use that in the future....
Anyway, here's the agent's view on this: the client has probably approached them and given the agency a budget of x to get someone placed.
The agency have seen you coming a mile off and when you said you were happy with rate y, they jumped for joy and offered you it, knowing that they were creaming a lovely, lovely margin (i.e. x minus y)
Now, it's clearly in the interests of the agency for the client not to know this (or, in the case of large organisations, other contractors). So they'll tell you it's not professional to discuss it. Hell, you're new to this game and don't know any better. Like I said, they saw you coming. That phrase is tough but true.
But you've gone and innocently mentioned it, and I don't think there's anything wrong in that - it's your business and your right to disclose it if you see fit. But the client has thought:
"Hang on! They're taking a ****load for not doing much at all, I expected the majority of that to go to the guy hired to do the work"
They've picked up the phone and gone nuclear on them. That's ****ed off/embarrassed the agency so they've now started threatening you.
Can they terminate your contract? Possibly, but they'd need just cause so I too recommend keeping your client in the loop at all times.
Sure, you'll probably never work through that agency again, but with friends like them who needs enemies?
You're new to this game, and yes, it can be a game. They'll be a few more tricks you'll pick up on the journey.