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Ask which sets can be selected
A statement that each of four units has inclusion chance 1/2 describes marginal probabilities. It does not say whether all six size-two subsets are equally likely. Those complete sample-set probabilities determine the design.
Use two possible paired samples
Selecting AC or BD with probability 1/2 each gives each unit chance 1/2. It excludes AB, AD, BC and CD. The size-two simple random design instead assigns all six subsets probability 1/6.
Keep unbiasedness separate from variance
With values 2,4,6,8 in labelled order, the AC-or-BD mean is 4 or 6, centered at 5 with variance 1. The simple random mean is also centered at 5 but has variance 5/3. The same population and equal marginal chances do not imply identical estimator uncertainty.
Record the full selection rule
For systematic or grouped selection, retain start rules, ordering and allowed combinations. Use the variance that follows from that design. Do not borrow the simple-random finite-population correction solely because every unit can be selected equally often.