PA34 DEP FROM MDW EXPRESSED CONFUSION WITH C90 CLASS B CLRNC.

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I CAME OUT OF MDW; VFR TO THE SW. WAS CUT LOOSE BY CHICAGO APCH. HAD BEEN FLYING 2000 FT PER CLRNC. I REQUESTED AN ATTEMPTED HDOF; GOT IT; AND WAS ASKED WHAT MY HEADING AND ALT WOULD BE; 238 DEGS AND 4500 FT. INSTRUCTED TO CLB TO 4500 FT; BUT NOT CLRED INTO CLASS B; WHERE THE EDGE WAS 3600 FT. CLBED FROM 2000 FT TO 3000 FT AND HELD IT THERE FOR 10 MI; ABOUT 3 MINS (15-25 NM DME FROM ORD). HAD LOTS OF TFC TO LOOK OUT FOR; HE WAS BUSY. DID NOT GET TO ASK IF CLRED INTO CLASS B. JUST AS I WAS EXITING THE 25 NM VEIL; THE CTLR SAYS; 'HEY; ARE YOU GOING TO GET AROUND TO CLBING TO 4500 FT AS I INSTRUCTED?' I REPLIED; 'YES; SIR; BUT YOU DID NOT CLR ME INTO CLASS B AND I WAS NOT ABOUT TO CLIP THE CORNER.' NO MAGIC 'CLRED INTO CLASS B.' 3 MINS HAD ELAPSED. HE REPLIED; 'WELL; I HAVE SOME MAGIC WORDS FOR YOU; SQUAWK VFR GOOD DAY!' MY PVT STUDENT WHO WAS ALONG FOR THE RIDE IS NOW EVEN MORE AFRAID TO TALK ON THE RADIO. CALLED UP CHICAGO APCH. THEY CORRECTED THE CTLR FOR NON STANDARD PHRASEOLOGY. THEY POINTED OUT THAT NO VFR PLT IS GOING TO CLB INTO CLASS B UNLESS CLRED.