にかこつけて means "using X as an excuse": someone does what they wanted to do anyway and points to X as the reason. It follows a noun – the excuse – and it is critical, of others or, half-joking, of yourself.
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I used the business trip as an excuse to do some sightseeing.
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He uses being busy as an excuse to do no housework at all.
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I look forward to cherry-blossom viewing as an excuse to drink in the afternoon.
The excuse takes , not . かこつける is the verb "to use as a pretext", written in kana; the kanji is rare.
にかこつけて or を口実に
, "with X as a pretext", means much the same and is the plainer phrase; its excuse takes を. にかこつけて is more bookish, and it stresses that the excuse was used opportunistically.
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She used a cold as an excuse to turn down the date.
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Under cover of entertaining clients, he ate at an expensive restaurant.
, "in the name of", names an official purpose, and
, "taking advantage of", exploits a situation rather than an excuse.
Lingaku