Contradiction with Psalms 56:3
Whereas Psalms 3:6 talks about not being afraid of thousands of people, Psalms 56:3 acknowledges fear and trusting in God when afraid.
Psalms 56:3: What time I am afraid, I will trust in thee.
Contradiction with Matthew 10:28
Psalms 3:6 expresses a lack of fear of pure numbers, while Matthew 10:28 advises fearing God over those who can kill the body.
Matthew 10:28: And fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell.
Contradiction with Proverbs 29:25
Psalms 3:6 encourages not fearing the multitude, but Proverbs 29:25 warns that fear of man brings a snare.
Proverbs 29:25: The fear of man bringeth a snare: but whoso putteth his trust in the LORD shall be safe. [safe: Heb. set on high]
Contradiction with 2 Timothy 1:7
While Psalms 3:6 concerns fearing numbers, 2 Timothy 1:7 contrasts by emphasizing God giving a spirit not of fear but of power.
2 Timothy 1:7: For God hath not given us the spirit of fear; but of power, and of love, and of a sound mind.
Contradiction with Isaiah 41:10
Psalms 3:6 presents fearless confidence against numerous adversaries, Isaiah 41:10 reassures not to fear because God is with us, recognizing that fear may occur.
Isaiah 41:10: Fear thou not; for I [am] with thee: be not dismayed; for I [am] thy God: I will strengthen thee; yea, I will help thee; yea, I will uphold thee with the right hand of my righteousness.