If I believe Christ died and rose for my salvation, why should I believe nothing can separate me from God?

Because Jesus promises eternal life to His sheep, saying they shall never perish and no one can pluck them out of His hand. Paul likewise includes the whole sphere of creation—angelic and satanic powers—so nothing can remove them. If you trust Christ's death and resurrection for salvation, you can trust that you are His and secure.

Les teaches that in John's gospel, chapter 10, verses 27-28, Jesus speaks especially to the nation of Israel using the term sheep: His sheep hear His voice, He knows them, and they follow Him. Jesus says He gives them eternal life, they shall never perish, and no one shall pluck them out of His hand. Les notes that the word "man" was added by translators, so he prefers to leave it out. He compares that word "any" with what Paul says in Romans 8, showing it includes the whole sphere of creation—not just man, but angelic powers and satanic powers—nothing can pluck them out of His hand. Les then applies it: if you can believe that God in Christ died and rose again for your salvation, then you should be able to believe these things, that you are 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.

Romans 8:38

For I am persuaded, that neither death, nor life, nor angels, nor principalities, nor powers, nor things present, nor things to come,

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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.