You can make a SSTO even without airbreathing, this is how the VentureStar would have worked. I think there are two benefits. One is that the oxygen takes up m

You can make a SSTO even without airbreathing, this is how the VentureStar would have worked. I think there are two benefits. One is that the oxygen takes up most of the fuel mass (e.g. the first stage of a Delta IV carries 173 tons of oxygen and 30 tons of hydrogen), so getting some from the atmosphere is a big weight saving. The other is that even if the air-breathing part on works in lowest part of the atmosphere, the denser parts of the atmosphere costs a lot of fuel because the rocket has to go slow and incurs more gravity drag. For the Falcon 9, first-stage separation occurs at Mach 6, roughly the same speed that the Skylon would switch from air-breathing to liquid oxygen. But in fact, the first stage is the biggest part of the rocket.