Simple, because the material technology required didn't exist. It was however, up to letting the Wrights build a petrol engine with an adequate power to weight ratio to permit flight.
I have a book printed in 1912 which contains a diagram of a gas turbine but its of a massive steel construction just like those steam turbines in the previous post. It took a great leap of imagination (and the development of Nickel steel alloys) to think that that gas turbine could become a jet engine and that's what Whittle had.
So how come the Italians were mucking about with the utterly useless Caproni Campini N1 in 1940 if the solution was so obvious? Even the Germans had taken advantage of Whittle's patent by 1936. What was Whittle's inventive step if it was not the first practical means of jet propulsion?