Feelings comprise a combination of thoughts, emotions and actions, and anxiety is a complicated blend of perception, thought, emotion and action.
When you believe a man with a gun is not dangerous because he dresses like a police officer and is interest in your protection, but at the same time you believe a gun is dangerous and the gun carrier will kill you, your strong irrational belief of danger most likely will prevail over your weak rational belief of protection. Strong convictions frequently lead to strong emotional reactions even when they are unfounded and probably false.
Strong Irrational Beliefs may override weak Rational Beliefs and create anxiety unrelated to social reality. REBT has emotive methods to challenge strong irrational beliefs and replace them with strong rational beliefs.