A CFI; WHILE TRAINING HER STUDENT IN DTW CLASS B AIRSPACE; WAS NOT FAMILIAR ENOUGH HERSELF WITH THE ENVIRONMENT AND CAUSED AN ACR TO GO AROUND.

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I UNDERESTIMATED MY STUDENT'S ABILITY TO COMMUNICATE IN THE ENVIRONMENT CAUSING COM DELAYS WHILE I TOLD HER WHAT TO SAY. IF I TRY TO BRING A PRIMARY STUDENT TO CLASS B AGAIN; AND I HEAR OTHER INCOMING ACFT; I WILL REQUEST TO LEAVE B AIRSPACE AND GO TO WILLOW RUN. I LEARNED THAT I MAY BE VECTORED ACROSS THE APCH PATHS OF 3 OTHER RWYS TO GET TO MY RWY; WHEN I USED TO ASSUME THIS COULD NEVER HAPPEN. MY STUDENT WAS VERY SLOW ABOUT TURNING BACK TO THE RWY; I THOUGHT WE SHOULD BE GOING TO. IN FACT; SHE THOUGHT I WAS WRONG; BUT DIDN'T SAY ANYTHING. I TOOK THE AIRPLANE AS SHE ENTERED THE TWR FREQ. I WAS NERVOUS THAT WE WERE TAKING TOO LONG TO CONTACT THE TWR. THE TWR ASKED IF WE HAD RWY 21L AND I SAID I THOUGHT I DID. THEN; WE WERE ADAMANTLY ASKED TO TURN TO 120 DEGS IMMEDIATELY. I DID HESITATE AT FIRST BECAUSE IT WOULD MEAN XING THE PATH OF AN AIRLINER (A B737?) THAT WAS ABOUT 1/3 MI AWAY AND ABOUT 800 FT ABOVE US. I HEARD THE AIRLINER TAKE THE CLB AND GO AROUND. I ALSO THINK THE ARPT DIAGRAMS IN THE AIRWAYS FACILITIES DIRECTORY COULD BE IMPROVED. I HAD COPIED THE DTW (DETROIT METRO) ARPT DIAGRAM AND HAD IT ON MY KNEEBOARD. THESE ARE GREAT TOOLS. BUT THE RWY NUMBERS ARE SQUEEZED TO FIT THE RWY WIDTH DEPICTED ON THE DIAGRAM. SO A BIGGER ARPT'S RWYS ARE EVEN NARROWER BECAUSE THE WHOLE ARPT HAS TO FIT ON THE SAME SIZE PAGE AS A SMALLER ARPT. I WOULD SUGGEST DOUBLING THE FONT SIZE ON RWY NUMBERS TO HELP PLTS READ THEM IN DIMLY LIT (NIGHT FLT) COCKPITS AND UNDER THE VIBRATION OF THE ENVIRONMENT.