ACR MLG ALT DEVIATION CROSSING RESTRICTION NOT MET.

Narrative

A VERBAL CONFLICT BTWN THE CTLR AND MYSELF RESULTED IN MY ACFT BEING LATE IN MEETING A XING RESTRICTION. WE WERE ON A FLT FROM MEX TO LAX AND APCHING JLI WE WERE TOLD TO CROSS JLI AT OR BELOW FL280 MAINTAIN FL240. WE CROSSED JLI AT FL280 AND CHANGED CTLRS. WE WERE ABOUT TO CONTINUE OUR DSCNT WHEN THE CTLR ASKED US WHY WE DIDN'T DSND TO FL240 OR RATHER I SHOULD SAY HE ASKED US WHY WE STOPPED AT FL280. ABOUT AT THIS POINT WE WERE CLRED TO 'CROSS 30 S OF PDZ AT 16000';' AND THEN IMMEDIATELY TOLD TO 'CROSS 20 S OF PDZ AT 16000'.' THE DISCUSSION; WHICH BECAME A VERBAL CONFLICT RE: THE FL280/FL240 CONTINUED. THE DISCUSSION BECAME EMBROILED AND PROLONGED AND MY ACFT WAS LATE IN MEETING THE 16000' RESTRICTION. I WAS DISTRACTED FROM MY COCKPIT MGMNT DUTIES AND I FEEL THE CTLR WAS DISTRACTED FROM HIS DUTIES. I HAVE CERTAINLY BEEN AROUND LONG ENOUGH TO KNOW THAT YOU SHOULD NOT TRY TO STRAIGHTEN OUT A MISUNDERSTANDING ON THE RADIO WAVES; BUT SHOULD USE THE TELEPHONE AFTER LNDG. BECAUSE I BECAME UPSET WITH WHAT I TOOK TO BE A CONDESCENDING ATTITUDE ON THE PART OF THE CTLR; I DID NOT PRACTICE WHAT I HAD LEARNED. EITHER THE CTLR OR MYSELF SHOULD HAVE SUGGESTED THE CONVERSATION BE CONTINUED VIA PHONE AT THE ONSET OF OUR DISCUSSION. NEXT TIME I WILL.