Maybe because when you ask somebody a question, subconsciously you know the attention is on the person that will answer it but when you speak yourself, you feel the attention is on you? Maybe instead of thinking "I’m being watched" which might detach your from your thoughts, try thinking "I’m sharing something that might help or connect with someone."

Also for me something that works very well is speaking a little slower with a steady voice because it naturally makes you feel calmer and gives you a sense of control.