Some critics of Latter-day Saint theology point to Num 23:19 and similar verses (1 Sam 15:29; Hos 11:9) as biblical proof against Mormon theology which states that God the Father is embodied and an exalted man (see the Prophet Joseph Smith’s King Follett Discourse from 1844, for e.g.) However, as with much biblical-based arguments forwarded by critics of LDS theology, such arguments are based on eisegesis.
The verse in question reads as follows:
God is not a man, that he should lie; neither the son of man, that he should repent: hath he said, and shall he not do it? Or hath he spoken, and shall he not make it good?
Firstly, one should note that these are the words of a false prophet, so it speaks volumes Evangelicals have to quote this verse. Notwithstanding, similar sentiments are found in 1 Sam 15:29 and Hos 11:19, so let us address this verse.
Secondly, it should be noted that Num 23:19 uses the Hebrew term, אִישׁ which is the comparative form of the word “man” in biblical Hebrew. It is used to compare one man to another (e.g. comparing an old man to a young man; a man to a woman).
Women, wives, and older men are all beings of the same species. The Hebrew word assumes that characteristic as the point of similarity on which it is used to make comparisons. In this passage, the attribute being compared through the use of the word אִישׁ is the trait of honesty, not manhood. This verse, and others like it, compare God as a man who does not lie with mortal men who do. The passage always assumes that God is a man.
Furthermore, the phrase translated “a son of man” in the next portion of the verse are taken from the Hebrew, בֶן־אָדָ֖ם, a phrase used to refer specifically to a mortal man, literally a descendant of Adam. The contrast is not between God and man, for that would have required use of the Hebrew word אָדָ֖ם alone.
Even these linguistic elements refuting the Evangelical appeal to this verse aside, the context of Num 23:19 (and other like-verses) are not the physiological nature of God, but his moral character--unlike fallen man, God does not lie nor does he stand in need of repentance. God's impeccable character is in view here.
A related text from the New Testament that critics sometimes appeal to is Rom 1:22:23:
Professing themselves to be wise, they become fools, and changed the glory of the uncorruptible God into an image made like to corruptible man, and to birds, and fourfooted beats, and creeping things.
As noted above, the Father (and the Son) has a glorified, incorruptible body and nature as opposed to corruptible, mortal men. Nothing in this passage, as understood contextually, and with proper understanding of Mormon theology, proves to be problematic. Further, Paul was condemning the pagans and those who are evil who exchanged God and His glory for things that aren’t real like idols (Psa 106:20; Jer 2:11). Their futile speculations were showing the pre-eminence of the Gospel of Jesus Christ as the culmination of God’s glory. He wasn’t teaching God’s alleged omnipresence or non-materiality which wouldn’t even make sense in the context of Rom 1:23.