Here is what happens the "very first" time the wave starts from the generator ...
FROM 1 TO 2 ...
Write that the Voltages of incident wave + reflected wave = voltage of transmitted wave : \$Wi+Wr = W12= 1 + (Z2-Z1)/(Z2+Z1)\$
\$=(Z2+Z1+Z2-Z1)/(Z2+Z1)\$ \$=2*Z2/(Z2+Z1)\$.
And when the wave come from the other side ...
FROM 2 to 1 ...
\$Wi+Wr = W21= 2*Z1/(Z2+Z1)\$.
