If a co-worker tells you that they don’t agree with your methods, or that they don’t think your role is important, first check to see if they understand your methods, or if they have worked with someone who performed your role. It is likely that his or her statement is a reflection of a personal bias, and not a reflection of your value to the organization.
For example, if your role is to measure, generate reports and metrics about the organization, your co-worker may say, “I trust my gut, I don’t think we should manage by the numbers.” Clearly, this person does not have the experience of using numbers. Yes, there are those who have blind faith in numbers, that is an extreme position and is a problem as well. But dismissing the use of metrics completely is prejudicial.
What if such a person is your boss? If you cannot turn the situation around and prove your value, you are headed for a lose-lose situation. It is a chance to hone your marketing skills and learn to work with a personality type that ruffles your feathers. Don’t lose that chance to improve. But don’t limit your career by not cutting your losses either.