MULTIPLE RWY OP INTERSECTING RWYS. ACR Y NON ADHERENCE TO ATC INSTRUCTIONS; HOLD SHORT OF INTERSECTING RWY. HAD LTSS FROM ACR X. PLTDEV.

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ACR X TKOF CLRNC ON RWY 4 LGA. STARTED THE TKOF AND AT ABOUT 100 KTS SAW AN ACR Y GO THROUGH THE INTXN OF RWY 4 AND 31. ACR Y WAS LNDG RWY 31 AND HAD ACKNOWLEDGED HE WOULD TURN OFF AT TXWY R. HE DID NOT AND CONTINUED THROUGH OUR INTXN. WE WERE TOLD TWICE TO CANCEL OUR TKOF CLRNC. VERY POOR TO DO WHEN IT'S BEEN 5 SECONDS OR MORE SINCE YOU WERE GIVEN CLRNC TO TKOF. (YOU DON'T CANCEL A TKOF CLRNC WHEN THE ACFT HAS HAD LONG ENOUGH TO ACCELERATE TO 100 KTS OR MORE!) NOT AT LGA WHERE THE RWY ENDS AND FLUSHING BAY BEGINS! ONCE I REALIZED WE COULD STOP I REJECTED THE TKOF AND SO STATED ON TWR FREQ. OTHER ACR ENDANGERED US BY NOT DOING AS HE SAID. BUT THE CTLR ADDED TO THAT BY FORCING (TRYING TO) US INTO AN ABORT. SUPPLEMENTAL INFO FROM ACN 237495: AT 100 KTS; LGA TWR CANCELLED ACR X TKOF CLRNC AND WE REJECTED THE TKOF; TURNED OFF AT TXWY P. ACR Y HAD MISSED HIS TURNOFF; ROLLING THROUGH THE INTXN OF RWYS 21 AND 31. BY THE TIME ACR X HAD REJECTED THE TKOF; ACR Y HAD CLRED THE INTXN. IN MY OPINION; ISSUING THE CANCELLATION; CAUSING US TO ABORT CORRECTED A MORE SERIOUS HAZARD THAN IF WE HAD CONTINUED TO TKOF. WE RETURNED TO THE GATE; COMPLIED WITH BRAKE COOLING PARAMETERS; HAD MAINT INSPECT THE BRAKES. FLT WAS RESUMED TO BUF WITHOUT FURTHER INCIDENT.