Date: 202106
Local time of day: 1801-2400
Location: ZZZ.ARTCC, US
Aircraft: B737 MAX 8
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class B ZZZ
ATC / advisory: Center ZZZ
Second aircraft: Commercial Fixed Wing
Reporter organization: Air Carrier
Reporter function: Pilot Flying; First Officer
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Human factors: Time Pressure; Situational Awareness; Communication Breakdown
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Detector: Person Air Traffic Control; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Separated Traffic; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Took Evasive Action
Contributing factors: Human Factors; Weather
Primary problem: Human Factors

Narrative: This was in a B737-8 MAX which is not selectable on the menu.  Inbound to ZZZ; deviating west of the arrival due to a severe TS over ZZZZZ and also another TS touching ZZZZZ1 along with multiple significant CB radar returns just west of our direct line to ZZZZZ1.  We checked in with ZZZ Center and descended to or level at FL340. We were made aware that our deviation west of the arrival was causing the Controller difficulty in de-conflicting our descent due to departing traffic which was below us and to my understanding west of us.  Very busy controller with no time to discuss options.  I was approaching the west edge (absolutely as close as possible) of the last significant CB when the Controller told us in an excited tone to turn right 15 degrees and descent to FL280 (or maybe 240; I don't recall now).  The CB was about 4 mile ahead and 2 miles across in both directions and 15 degrees right would put us straight through the middle of it.  I started an immediate right and tried to ask my First Officer to tell the Controller we had to have farther right; but he saw me turning and read back the 15 degree instruction.  The Controller was immediately on to two or three other calls.  I asked my First Officer to tell the Controller the heading that we needed to fly and about then the Controller noticed that we had turned a bit extra and shouted at us because apparently another aircraft was departing in the corridor between the last CB and the big TS.  I immediately corrected back and flew through the middle of the CB I was trying to avoid which was where the Controller wanted us in the first place.  I also paused my descent very briefly to verify with the Controller that we were going to be safe still and we agreed on a heading of north as we passed directly through the cell.  Fortunately; despite passing though the small cell with a solid yellow return; there was no significant turbulence and no injuries.  I don't believe we caused loss of separation and my intention was to coordinate and return to the desired heading as soon as possible. The frequency was too busy; departures probably should have been pushed farther west; I was trying to comply with the Controller's guidance as best I could while not creating a dangerous turbulence situation for my flight attendants and passengers.  The B737-8 MAX radar might be overly sensitive.  Had the Controller asked 30 seconds sooner we would have had time to coordinate; or a minute later we could have taken any heading.  In retrospect; we should have said we were unable to turn for another 6 miles; but given the urgency in the Controller's voice; I thought I was doing the right thing.Whenever an airplane is cleared to deviate for weather and is operating around thunderstorms and significant CBs; it seems like the Controller should always ask if you can accept a turn; not just assign a heading into the direction of the things we are avoiding.  Also; if there is any way to make these frequencies less congested; that would help also.  And finally; the other company's aircraft was apparently flying outbound and closer to our assigned arrival than we were comfortable with flying inbound.  Maybe ZZZ Center should develop and publish alternate Departure and Arrivals that could be assigned for weather avoidance as widespread thunderstorms are so common in this area.




Synopsis: Air carrier First Officer reported a weather deviation was required but the very busy ATC controller was unable to accommodate the request. A heading deviation and airborne conflict may have resulted.