How do we know that Christ was incapable of sinning?

The doctrine of Christ's impeccability is rooted in His divine nature, which informs His capability to remain untainted by sin. According to James 1:13, 'God cannot be tempted with evil,' asserting that true divinity lacks susceptibility to sin. Since Christ is fully God and fully man, His divine nature fundamentally negates any possibility of sin. By being God manifest in flesh (1 Timothy 3:16), He possesses attributes that are inherently incompatible with sin.

Moreover, Hebrews 7:26 describes Christ as 'holy, harmless, undefiled, separate from sinners.' This designation emphasizes that, unlike any other created being, Christ's divine essence keeps Him untarnished by the sinful environment surrounding Him. As such, not only was Christ able to overcome every temptation He faced, but He was also incapable of falling into sin due to His divine authority and the perfect union of His natures, making the idea of Him sinning not just unlikely, but an impossibility.