What does it mean to deny yourself?

Some teach that Christians need to deny themselves as if their “self” is bad. But in Matthew 16:24-26, Jesus is not speaking of an ongoing denial of self. He is talking about a one-time decision to deny our old self (in Adam) and become a new self (in Christ). Now that you are the new self, you should not deny your new self, your new heart, or your new desires. You should instead count yourself dead to sin and alive to God (Romans 6:11).