This is a very common myth that has been largely popularized by cartoons. In the after life people are seen flying around with wings attached, carrying harps and resting on clouds. Bible does say we will be like angels in some ways – the fallen angels like fallen man will be judged someday by God, and for both there is no marital relationship in the eternal realm. Nowhere does it say we will become angelic beings. The Bible does say in heaven we will be higher than the angels and never once mentions the two groups as being interchangeable.
Scripture also tells us: “Do you not know that we will judge angels. How much more, things that pertain to this life?”(1 Corinthians 6:3). However, that verse could be referring to the rebellious angels who chose to follow Satan, but it still infers that our status after death will be above that of the angels.
At the Rapture, Jesus “will transform our lowly body that it may be conformed to His glorious body”:
“For our citizenship is in heaven, from which we also eagerly wait for the Savior, the Lord Jesus Christ, who will transform our lowly body that it may be conformed to His glorious body, according to the working by which He is able even to subdue all things to Himself” (Philippians 3:20-21).
“Beloved, now we are children of God; and it has not yet been revealed what we shall be, but we know that when He is revealed, we shall be like Him, for we shall see Him as He is” (1 John 3:2).