Can God make someone equal to Himself? The simple answer is no. But people sometimes ask that if God can do everything, then why can’t He produce someone that is His equal? First of all, God cannot do everything. He cannot lie (Titus 1:2). He cannot stop being God because He is eternal in the past and the future (Psalm 90:2). So, to stop existing would mean He was not eternal in the future. Furthermore, God cannot un-create Himself and then create Himself out of nothing. God cannot do anything that is logically impossible.
But it is not that logic is a separate category from God to which He must submit. Instead, from the Christian perspective, logic is part of the mind of God – the perfect and proper understanding and reasoning in all categories of thought. This is because He is eternal (Psalm 90:2), unchanging (Mal. 3:6), and knows all things (1 John 3:20). He is also transcendent and noncontingent. Transcendence means that He does not depend upon anything external to Himself for His existence and that The material world does not restrict him. He is independent of everything from forever ago. This is related to His aseity – His eternal, independent existence. That is why there is none like Him. So, God cannot violate His own nature. In other words, He is what He is and cannot be what He is not. He is eternal and alone in His perfect nature. Therefore, He cannot violate His own nature and lie or stop being God.
In Christianity, God is a Trinity. He is one eternal being who exists as three simultaneous, coeternal, distinct persons: the Father, the Son, and the Holy Spirit. The persons are not like humans, where each is also a being. Instead, when we say “persons” in the context of the Trinity, we mean the characteristics of having a will, being self-aware, aware of others, can love, hate, think, reason, etc. The Trinity is three of these, not three beings, not three Gods. After all, God is a triune being. If any of the three persons were removed, God would not be God. Think of a cube. It has height, width, and depth. If any one of those three aspects were removed, the cube could not exist. For more on this, please see the Trinity Chart.
So when we look at God and ask if He can create someone equal to Himself, then that would be logically impossible because part of what it means to be Himself is to be noncreated. Therefore, for God to create someone equal to Himself would be impossible because it would mean He would have to create a noncreated being. But that makes no sense.