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To act assuredly and boldly because your reasoning is sound and just. Often used in reference to speaking.
Positive
我方代表理直气壮地驳斥了对方的谬论 | Wǒ fāng dàibiǎo lǐzhíqìzhuàng de bóchì le duìfāng de miùlùn
Our representative confidently refuted the other side's absurd theories
[Source]
我们要理直气壮地倡导科学，反对迷信 | Wǒmen yào lǐzhíqìzhuàng de chàngdǎo kēxué, fǎnduì míxìn
We must firmly advocate science and oppose superstition
[Source]
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This is an HSK chengyu
《古今小说》(Gǔ Jīn Xiǎo Shuō), a collection of novellas by Míng Dynasty (明, 1368 - 1644) author 冯梦龙 (Féng Mèng Lóng). The work was written in 白话 (bái huà, or the common vernacular) as opposed to the classical Chinese that was standard for written works at the time, and it is known in English as "Stories Old and New" or "Stories to Enlighten the World"
I'm unable to find consistent evidence of a story for this chengyu, so I won't be translating it here