Why should a Christian believe that nothing can separate them from God?

Because if a person can believe the greater truth that God in Christ died and rose again for their salvation, they should be able to believe the lesser truth that nothing can separate them from God. Jesus declared no one can pluck His sheep out of His hand, and Paul extends this to all creation, including angelic and satanic powers.

Les explains that in John 10:27-28, Jesus says His sheep hear His voice, He knows them, they follow Him, and He gives them eternal life; they shall never perish, and no one can pluck them out of His hand. Les notes that the word “man” in verse 28 was added by translators, so he prefers to leave it out, making it “neither shall any pluck them out of my hand.” Comparing “any” with Romans 8, Les says this includes the whole sphere of creation—not just man, but angelic powers and satanic powers—nothing can pluck them out of His hand. The application is that if you can believe God in Christ died and rose again for your salvation, then you should be able to believe these things, that you’re His.

John 10:28

And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand.

If I believe Jesus died and rose for my salvation, why should I believe nothing can pluck me out of His hand?

Because Jesus promised His sheep eternal life, declaring they shall never perish and no one can pluck them out of His hand. Paul includes the whole sphere of creation—angelic, satanic, and human powers—as unable to separate them. If you believe God in Christ died and rose for your salvation, you can believe you are His.