C-Betting on Flops that Missed Both You and Your Opponents?

From Analytical No-Limit Holdem:

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I don’t understand the author’s point very well here on why you should tend to c-bet pairs and ace highs (as well as weaker hands that are more likely dominated if they hit). How can an opponent make profit by going all in with aces and pairs against our c-bet?

Question: Why not check the flop in position with pairs and ace high hands? If you have hands like these (that are both weak but still probably best), shouldn’t your objective be to get to the river as cheaply as possible (and/or induce a turn or river bluff from your opponent for more value)?

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