All the replies about wings and air are leaving out that jets breath air. There is a point where jet engines would just go out if you fly too high.
BUT the shuttle didn’t have jets, it had rockets. There simply wasn’t enough fuel in the shuttle to make orbit with it’s rockets (even flying like a jet to the upper atmosphere). There was not enough thrust to get off the ground with more fuel without the boosters. Once you add the boosters and external tank, there isn’t enough lifting surface to fly like a plane.
There is a space plane design that switches from atmosphere to onboard oxygen as it goes higher, but it isn’t real yet because it’s a very hard balance to get right and may be impossible.
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