You’re not going to expect this answer, but YES, there are things God cannot do. And we actually ought to be thankful for that! Now, I can imagine you loudly asking your screen, “How can GOD not be able to do something?”
Just to get this out of the way, it is true that God cannot do anything that is literally not possible in reality—such as creating a triangle with only two sides or a married bachelor. Just because words can be strung together does not make them possible. These are contradictions and truly impossible in reality.
Beyond that, yes, God is omnipotent and do anything—except one thing: God cannot go against His nature or His character.
You know how you aren’t the same person you are today as you were five or ten years ago? You’ve physically grown older, your interests may have changed, maybe you've moved cities. Perhaps you used to love to paint and now you’re more into skiing. Maybe you used to have one group of friends but now you have all new ones.
Humans will always change, but God remains the same. God is the same today as He was yesterday, and He will be the same tomorrow (Hebrews 13:8). Therefore, His nature, or what makes God who He is, will always stay the same.
"Heaven and earth will pass away, but my words will not pass away." —Matthew 24:35
God's unchanging nature is cool for multiple reasons, but for one, God cannot be fickle. He isn’t like the gods of Greek mythology who were so temperamental that people had to walk on egg shells because they didn’t know what would upset or please their gods that day.
"But to all who did receive him, who believed in his name, he gave the right to become children of God..." —John 1:12
Our God doesn't change the rules on humanity to see if people can keep up. We have no need to fear that God will change His desires or expectations (Numbers 23:19).
God’s nature is to be 100% holy (Isaiah 6:3). He cannot sin nor tolerate sin. He is the definition of perfection. Speaking of Jesus, Hebrews 4:15 says, "For we do not have a high priest who is unable to sympathize with our weaknesses, but one who in every respect has been tempted as we are, yet without sin." Titus 1:2 tells us that God cannot lie, therefore He is completely trustworthy and will never break His promises (2 Corinthians 1:20; 1 John 1:9).
"He who dwells in the shelter of the Most High will abide in the shadow of the Almighty. I will say to the Lord, 'My refuge and my fortress, my God, in whom I trust.' —Psalm 91:1-2
Our holy God wants a relationship with us, yet He cannot tolerate sin in His presence, so He provided a Savior. Without Jesus Christ coming to earth and paying the penalty for our sin, we would have been without hope (1 John 2:2). We cannot be perfect, yet God is perfect. Without God's loving us enough to send Jesus to die for our sins, we could never draw near to God (John 3:16).
It would go against God’s nature to say, "Nevermind, your sin is fine," because sin is against the very essence of who God is. And God cannot go against Who He is (Mark 10:25-27).
"God is not man, that he should lie, or a son of man, that he should change his mind. Has he said, and will he not do it? Or has he spoken, and will he not fulfill it?" —Numbers 23:19
God created the heavens and the earth and everything in between (Jeremiah 32:17). Things which seem impossible to us are absolutely possible for God (Genesis 18:14). To even scratch the surface of understanding what God is capable of would take a human being a hundred lifetimes or more.
And we’re not just talking sheer power (though He has plenty!), but this is the creative majesty of the universe we're talking about. God created the rules of physics, chemistry, and biology—and He did it in an incredibly beautiful and creative way! No science fiction author or screenwriter could ever invent creatures as weird as ones we’re still discovering in our world today.
God could have chosen to give humans just the basics—only the plants and animals we needed for survival. Instead, He designed such an intricate, splendor-filled world of colors and smells and sensations that would exceed our imaginations. We have mountains and oceans and crystals and flowers and crazy lifeforms that make us shake our heads in wonder...
God and His ability to do all things is awe-inspiring. The more we study Him, the more we learn what He can and has done, the more we have the opportunity to be blown away by His holy, loving, and creative nature.
"Great is our Lord, and abundant in power; his understanding is beyond measure." —Psalm 147:5
Yes, there is one thing God cannot do: He cannot go against His nature. God is holy—the definition of perfection—and He cannot do anything that is less than holy.
Heidi Joelle spends her days staring at paperwork and making sure it is where it is supposed to be, how it is supposed to be, when it is supposed to be. And then she comes home and makes sure the porky little dog isn't eating a trashcan. Between these two events, she tries to learn and see as much of the world around her as possible.