Remember the #1 rule of communication? Begin with the audience in mind. There are many ways to express your point honestly and directly without attempting to transfer your anxiety to the other.
Here's an example:
You're new at a job and a demanding, disorganized client asks for something right away. The request falls to you as it is part of your responsibilities. You come out of a meeting to find an email from a colleague with the request and realize you have no time to meet the deadline. Your anxiety skyrockets. You shoot off an email criticizing your new colleague for the way the request was handled. Outcome: Poor first impression of you and work not managed.
How else can you approach this situation? Pick up the phone, seek to understand how the situation came about, manage your anxiety with a few deep breaths before explaining where you are and why you may need help. People will respect vulnerability before what could be perceived as rudeness.
Few simple things to remember for the truth tellers out there:
1. Is your audience ready for what you need to tell them?
2. Are you managing your own anxiety before sending that email or making that comment (i.e. think before you send/speak)?
3. What is your relationship to the person you are addressing (new colleague, friend, spouse, superior, subordinate, peer)? How will that affect the message? How can you tailor it to your audience to get the job done?
4. Play for the long-term relationship. Once you've built trust, you can be more direct the first time around and people will put it in context.