I remember that when the Space Shuttle first came out, everyone was excited because it could land like an airplane. Well, why can’t we build a spacecraft that takes off like a plane as well? What sort of engineering difficulties stand in the way of constructing a plane that flies into the upper atmosphere, deploys rocket boosters, jumps into low earth orbit, and makes international flights faster than cross-town traffic?
When you go straight up the drag drops a lot faster than if you go up at an angle. Means you need less fuel, which makes you either lighter or able to put more stuff in orbit.
The airplane idea has value because you use the oxygen in the atmosphere instead of dragging it along with you. The recent scramjet testing is tied to that.
The Pegasus is along the same lines - it is lifted to 40,000 ft altitude by a conventional airplane and launched there. Also Burt Rutan’s Spaceship One uses the same method.
Most rockets use vertical takeoff because horizontal flight requires wings. For a launch vehicle, wings don’t provide any additional energy to reach orbit. It’s just dead weight. The Shuttle’s wings are for landing, a substitute for a parachute.
Skylon is a similar concept.