In Israel's last election cycle, there was much mention of the word hitnatzel התנצל - to apologize. This is the hitpael form of the root נצל. In its other forms, the root has very different meanings. The piel form nitzel ניצל, means "to exploit" or "to utilize". And the hifil form, hitzil הציל, means "to rescue, save". Considering how loaded with emotions those words are, it's understandable the desire to make a connection. For example, in this blog post, Avidan Freedman writes:
And if the word for apologizing (lehitnatzel) wasn't a reflexive form of the word for ‘taking advantage of’ (lenatzel), implying that someone who apologizes is essentially taking advantage of himself, (thus transgressing the 1st commandment of Israeliness ‘Thou Shalt Not Be A Freyer”), perhaps “No More Apologizing” would be a less attractive slogan.
If this is so, then the root of apologizing is not a way to take advantage of ourselves, but a way to bring ourselves salvation.