A PA28 INSTRUCTOR PLT WITH STUDENT TAKES THE RWY WHEN SIMPLY ASKED BY THE TWR CTLR IF THEY COULD ACCEPT AN IMMEDIATE TKOF AT NZY; CA.

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TWR ASKED IF I COULD ACCEPT AN IMMEDIATE TKOF. I ACKNOWLEDGED THAT I COULD AND WAS CLRED; I THOUGHT. TWR WAS COMMUNICATING TO ANOTHER ACFT WITH SIMILAR CALL SIGN. WHEN TWR SAW MY ACFT TAKE THE ACTIVE SHE CANCELED THE TKOF CLRNC; I EXITED THE RWY AND WAS INFORMED OF MY ERROR. OBVIOUSLY; THIS WAS MY MISTAKE. CONTRIBUTING FACTORS; INCLUDE THE FOLLOWING: I AM A LOW TIME INSTRUCTOR AND THIS WAS MY FIRST FLT WITH THIS STUDENT. OCCURRENCE HAPPENED AT NZY WHERE MIL TFC USES ONE FREQ AND CIVIL ACFT USE ANOTHER. HAD I HEARD THE MIL TFC ACKNOWLEDGE THE TWR; THIS WOULD NOT HAVE HAPPENED. HUMAN FACTORS WERE: I WAS CONCERNED/PREOCCUPIED WITH THE NEW STUDENT AND THE WX WHICH WAS MARGINAL. ALTHOUGH LEGAL I THINK IT WOULD HAVE BEEN BETTER NOT TO FLY IN MARGINAL CONDITIONS WITH A STUDENT. IT WAS A BAD EXAMPLE I WILL NOT REPEAT. TO KEEP THIS FROM EVER REOCCURRING; I MAKE SURE I REPEAT CLRNCS FULLY AND GIVE ATC SUFFICIENT OPPORTUNITY/TIME TO CORRECT ANY MISTAKES/MISREADS ON MINE OR THEIR PART. I ALSO AM MORE CONSCIOUS OF OTHER ACFT ESPECIALLY WHEN ACCEPTING MIDFIELD DEPS.