Though I will shortly point out four things that God cannot do, I agree with the Westminster Confession of 1647 that my purpose in life is to glorify God and enjoy Him forever. That said, I am not attempting to diminish His glory by examining this topic. On the contrary, I would say that these reasons help ascribe the glory to Him He deserves.
Here’s the first one: God cannot sin.
“For I am the LORD your God… I am holy” Leviticus 11:44 CSB
“…it is impossible for God to lie” Hebrews 6:18 CSB
I’ve had some intense reactions to this one. Sometimes when I say that God cannot sin, people will declare that it’s not that He can’t, but that He won’t. Others are adamant that because he won’t, and because God keeps His promises, He can’t.
Either way, God can’t and/or won’t sin.
The second one is that God cannot learn.
I assume there are libraries in heaven. If there are, He doesn’t need to read their books.
“Our Lord is great, vast in power; His understanding is infinite.” Psalm 147:5 CSB
“Do you not know? Have you not heard? Yahweh is the everlasting God, the Creator of the whole earth. He never grows faint or weary; there is no limit to His understanding.” Isaiah 40:28 CSB
Since God is omniscient, there is nothing He does not know. Not only does He know the complete past, present, and future, He knows counterfactuals—that is, He even knows would could have been.
The third is that God cannot commit suicide or cease to exist.
“Before the mountains were born, before You gave birth to the earth and the world, from eternity to eternity, You are God.” Psalm 90:2 CSB
“He remains faithful, for He cannot deny Himself” 2 Timothy 2:13 CSB
God is eternal and omnipotent. God created death, and therefore it has no power over Him. There is nothing that exists that can cause God not to exist.
Number four is that God cannot create a being more powerful or equal to Himself.
“There is no one holy like the LORD. There is no one besides You! And there is no rock like our God.” 1 Samuel 2:2 CSB
Since God is the absolute sovereign of the universe, He cannot create a being more powerful than Himself.
Can you think of anymore?