And it repented the LORD that he had made man on the earth, and it
grieved him at his heart. (Genesis 6:6, KJV)
וַיִּנָּ֣חֶם יְהוָ֔ה כִּֽי־עָשָׂ֥ה אֶת־הָֽאָדָ֖ם בָּאָ֑רֶץ
וַיִּתְעַצֵּ֖ב אֶל־לִבֹּֽו׃ (TR)
This Hebrew word וַיִּנָּ֣חֶם (way·yin·nā·ḥem / H5162) is a difficult one to properly translate. It is in the Hebrew Niphal/Nifal form, which happens to be passive voice, and yet it can mean a number of things which are not passive in English.
If we say God "was sorry," we convert it to an adjective (plus a linking verb). If we say He "repented" or "regretted" or "rued the day," we convert it to active voice. If we say God "comforted Himself" or "consoled Himself" we make it reflexive. We could, of course, say He "was consoled" or "was comforted"--and those are passive voice verbs, but those do not do justice to the Hebrew concept here. And we cannot even possibly say God "was regretted" or "was repented"--these verbs have no passive voice forms in English that could apply to this context.
Translators, therefore, have a hard time with this verse. It's nearly impossible to get it right.
One of the possible translations for this Hebrew word would actually be: "was moved to pity."
It is always possible, as well, that when looking at Hebrew from Genesis, one of the earliest books of the Bible to be written, the meaning was slightly different from what it may have later evolved to mean. Languages do evolve. Just 150 years ago, if I called you "conservative," it would have meant something more like "preservative," and might even have hinted at "stingy"--hardly a compliment! Nowadays, many Christians would like to be thought "conservative."
Knowing that God knows the future as well as if it were already the past tells us that it would be impossible for God to actually regret something that He has done. The KJV translation here is awkward "it repented the LORD." It what? That doesn't even make sense in English. "Repent" is not one of those words we can apply in a passive sense like this.
The real trouble is that English lacks an equivalent word to this Hebrew concept. Because of this, we need to look at the broader picture, applying what we know from other Biblical passages to this one. Is it possible for God to feel sorrow or grief?
And grieve not the holy Spirit of God, whereby ye are sealed unto the day of redemption. (Ephesians 4:30, KJV)
Apparently it is.
I would submit that the story of Genesis 6:6 is essentially the same as seeing Jesus brought to tears in John 11:35: God felt sorrow.
The translation of this verse is problematic because of lack of full equivalence between Hebrew and English for this crucial verb.
I would submit that this verse might more clearly be translated as:
And Jehovah was moved to sorrow because He had made man on the earth, and He felt grieved at heart.