“If we measure a distance x at time t from Earth to the spaceship, then we must measure a distance of -x from the spaceship to the twin.” Who is “we” here? If “we” are both using the Earth’s reference frame it is true. But those distances “at time t” are between the Earth and spaceship at the same time from the point of view of the Earth. And when someone moving with the spaceship measures the distance they get a smaller value because what the Earth thinks of as at the same time as when Earth’s clock said time t is to the spaceship actually not at the same time but somewhat earlier or later (depending of direction of motion and due to the different corrections they make for light travel time by using the same speed of light despite the fact that they are moving relative to one another). When the outbound spaceship thinks it is at the same time as the Earth clock showing time t it is actually earlier so the distance between the Earth’s clock showing time t and the spaceship at what it thinks is the same time is less than the Earth’s idea of that distance.
Source: (508) Alan Cooper’s answer to There is no twin paradox if, when resolving, one is assuming that the Earth is at rest. How do the diagrams compare with the Earth(and earthbound twin)making the voyage and the shuttle/travelling twin at rest? – Quora