Date: 201709
Local time of day: 1201-1800
Location: ZZZ.ARTCC, US
Flight conditions: Mixed
Weather elements / visibility: Thunderstorm; Turbulence; 10
Light: Daylight
Aircraft: EMB-505 / Phenom 300
Operator: Personal
Operating under: Part 91
Flight plan: IFR
Mission: Training
Flight phase: Descent
Airspace: Class A ZZZ
ATC / advisory: Center ZZZ
Reporter organization: Personal
Reporter function: Instructor; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Flight Instructor
Human factors: Situational Awareness; Communication Breakdown
Second reporter function: Trainee; Pilot Not Flying
Anomaly: ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Took Evasive Action
Contributing factors: Human Factors; Weather
Primary problem: Weather

Narrative: Instructor/Mentor Pilot was acting [as] PF. During the descent briefing the PF/IP informed the PIT (Pilot in Training) that the weather over the arrival was deteriorating. XM Weather and Active Weather Radar was painting numerous cells starting to top at FL400. Literally the entire area was bubbling up with convective activity creating a dangerous situation. Descent/Approach briefing completed the THREATS were clearly outlined as Severe Weather both on the arrival and the wind conditions at the field.[While cruising] at FL450 the Controller issued a clearance to descend to FL400. PIT (Pilot in Training) doing the radios advised the Controller to stand by. After conferring with the IP/PF both pilots agreed it was much safer to stay at FL450. PIT reported to [ATC] that we wished to stay at FL450 until we passed the worst of the weather. The Controller DEMANDED a descent. Again the PIT with authorization from the PF/IP advised we were unable to descend. The Controller then assigned us a heading of 210 and demanded a descent. The PF/IP made the call to begin the descent and try to help the Controller out. We accepted the 210 heading and descend to FL350. We heard the Controller ask for an expeditious descent through FL370. Upon rolling out on the heading of 210 we were closing in on a large cell. We asked the Controller for a 230/240 heading for weather. When we turned to that heading; it was obvious we were going to go through the tops of another cell.Now unable to get on the radio due to numerous aircraft requesting VECTORS FOR WEATHER we turned to a SAFE heading of 260 and at first break in the radio; advised the Controller we now needed a 260 heading for weather. The Controller replied with 'You are not cleared for a 260 heading'. We again advised 'sir; we need the 260 heading for weather!' again the Controller said 'you are not cleared on to that heading'. This left the crew no option but to [override the Controller] for safety. We immediately took a picture of the weather radar and view out of the window showing the imminent threat. Pilots should keep in mind that an XM Weather image may be 20-30 [minutes] old and that what matters most is the image out of the window and on the weather radar. The atmosphere had clearly reached a boiling point making safe flight very much in doubt. If we had the time we would have squawked 7700 prior to making the turn to 260 but it is always Aviate; Navigate and then Communicate. Didn't have time in a dynamic situation. I stand behind the decisions we took as a crew to have a safe conclusion to our flight.


Second narrative: [Report narrative contained no additional information.]


Synopsis: EMB-505 flight crew reported using Captain's authority to circumnavigate an area of thunderstorms.