A C172 PLT COMPLETED A TKOF ON TXWY E AFTER MISUNDERSTANDING ATC'S CLRNC FOR TKOF ON RWY 25R FROM TXWY E.

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I WAS CLRED BY GND TO RWY 25L VIA TXWY E; HOLD SHORT OF RWY 25R. UPON HOLDING SHORT; GND TOLD ME TO SWITCH TO TWR FREQ FOR DEP FROM CURRENT POS. I CONTACTED TWR; UNAWARE HE WANTED ME TO DEPART ON RWY 25R. I ASKED TO CROSS RWY 25R VIA TXWY E TO RWY 25L AND HE CORRECTED ME; SAYING I WANTED A DEP. I SAID YES I WANTED A DEP; AND HE TOLD ME TO HOLD SHORT. THEN HE ISSUED A CLRNC FOR TXWY E AT RWY 25R. I QUESTIONED; SAYING 'YOU WANT ME TO TAKE OFF 'ON' TXWY E AND MAKE L TURNS FOR LNDG ON RWY 25L?' HE AFFIRMED MY QUESTION; SO I READ BACK THE SAME THING AGAIN; CLRED THE TXWYS AND RWYS FOR TFC AND DEPARTED ON TXWY E. NO OTHER ACFT WERE WITHIN A DISTANCE TO THE POINT OF COMPROMISING SAFETY. AFTER THE TWR TOLD ME; 'THAT'S NOT WHAT I WANTED YOU TO DO;' I FOLLOWED INSTRUCTIONS AND TAXIED BACK TO THE RAMP. IN MY FAULT; I WAS AWARE THAT OPS DON'T USUALLY; IF EVER; AUTHORIZE A TAXI TKOF CLRNC; BUT THE AIRSPACE WAS BUSY AND I KNEW THEY HAD SPECIAL OPS BEING CONDUCTED; SO UPON SECOND CONFIRMATION I DEPARTED. THE TWR DID NOT PHRASE MY CLRNC CORRECTLY AND DID NOT CATCH THE ERROR IN MY READBACKS. I BELIEVE BOTH OF US WERE AT FAULT IN THE INCIDENT.