Pins on students flutes do not come out as easy as on pro flutes. Plus they can be bent, have rust in them, making the removal process more difficult. If you've already hit it with a punch, depending on how hard and how many times, you may have peened the end over and it will no longer go through the hole. When that happens, you may need to grind it off slightly leaving a nice flat surface. Then with a proper punch tool, line it up perfectly and give it a good solid hit. Miss and you start over again. Do it too many and there's nothing left to grind!
Sometime the key side is soldered. Try taking the other side off, Probably two pins, one for the clutch and one for the kicker. If they are going to solder anything, it would be either the Bb on the LH and sometimes the F# on the RH.
If there is rust in there, you can put some penetrating oil in there and heat the tube over an alcohol lamp. If you get rust oozing out, you'll definitely will find out that way.