I don't know of anywhere in scripture where we are told precisely that we must die to ourselves. But we are told in 1 Peter 2:24 that our new life in Christ includes death to sins.
And in Matt 16:24, Mark 8:34, and Luke 9:23, Jesus' words are recorded: "If anyone would come after me, he must deny himself and take up his cross and follow me." Luke includes "daily".
Add to these Romans 12 and many other passages, and I have no trouble believing that I must "die to myself".
But, honestly, self-denial of any measure, let alone dying to myself is quite a leap for me. It's unnatural. My thoughts are habitually bent toward self-preservation and self-satisfaction. So much so, that I (cunningly, I imagine) try to use my own selfishness to motivate me toward righteousness.
Righteousness and obedience to God truly are rewarding not only in eternity, but now. Though, not necessarily in the same ways that we typically enjoy life. But fellowship with God, enabled and strengthened by submission to him, is joyous beyond all the world has to offer. Psalms relentlessly exhorts us with "Rejoice in the Lord!" So there is some reasoned thought behind attempting to find pleasure in the Lord rather than in the world.
Does "deny himself" mean to seek experiences of suffering and misery or reject all opportunities for pleasure? Rather, does it mean:
- Do not conform any longer to the pattern of this world, but be transformed by the renewing of your mind. Then you will be able to test and approve what God's will is—his good, pleasing and perfect will.
~ Romans 12:2