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Motion is relative. We can make the frame-independent
statement that one twin has an outbound velocity that
is different from his inbound velocity. That twin's
two velocities are different RELATIVE TO EACH OTHER.
The stay-at-home twin has no such velocity-difference.
That's all that need be said in order to break the
alleged symmetry, and SR has no problem saying that.
http://www.monmouth.com/~jsd/physics/twins.htm