Unable to choose the correct meaning of betray

GRE Verbal Problem Solving
1

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In this question, if I take betray to mean ‘reveal unintentionally’, follow fits the second blank. But if I take betray to mean ‘desert in times of need’, brandish fits the second blank. Is there something I’m missing? How can I choose the correct option in this scenario?

Also, is there anything wrong with the way I used the math strategy? The sentence before the second blank says that ‘he doesn’t follow a fixed set of principles’. After that there is ‘however’. So, won’t the opposite of that be ‘piously follow political principles’?

Thanks in advance.

2

what makes this question difficult is that ‘pious’ is not a synonym of devout here but rather a synonym of insincere/hypocritical. so the answer is brandish.

your three pairings are:
idealistic—strategic (+, -)
brandish–betray (+, -)
unchanging higher purpose–deeply felt moral code (+, +)

3

What do you do when you’re torn between different meanings of a word in a sentence?