Why does decimation make a system time variant?
HINT:
Think about the following situation: you have an input signal with alternating ones and zeros, and you decimate by a factor of $2$. Now shift the input signal by one sample and compute a new output signal by decimating by a factor of $2$. Is the output signal a shifted version of the previous output signal? If the system is time-invariant, shifting the input signal causes the output signal to shift by the same amount.