The turbine removes energy from the exhaust gases in order to power the compressor. In no way does the turbine provide thrust, so the propeller analogy is wrong!
I beg to differ!. Sure the turbine removes energy to drive the compressor, but if that was all it did there wouldn't be any thrust. The whole essence of a jet engine, at least as I understand it, is that the machine accelerates the air going in at the front to give it increased momentum when it leaves the engine. From what part (of a pure turbojet) does it get that increased velocity if it isn't the turbine?
To quote from Rolls Royce "the jet engine"
From C to D (expansion through turbine and nozzle on a working cycle chart) the gases resulting from combustion expand through the turbine and jet pipe back to atmosphere. During this part of the cycle some of the energy in the expanding gases is turned into mechanical power by the turbine and the remainder, on its discharge to atmosphere, provides the propulsive jet.
Italics are my explanatory addition, bold is my emphasis