Intuition is a Process, not an Identity
This might be a strange thing to say, given that I am a person who actually identifies myself as an intuitive in everything from business cards to website banners to casual conversation, but I do love a distinction worth making.
I'm a professional intuitive. I'm also an intuitive in the sense that I have a preference for using intuition. Calling myself an intuitive reveals a lot about how I personally move through the world, gather information, and make decisions. I tend to make heavy use of intuitive processes on a daily basis, but that doesn't mean that I think intuition is the only valuable process. I also use my five physical senses to gather information and I use rational processes constantly to assess and understand things.
I love to call myself an intuitive, perhaps mostly because then I don't have to call myself a psychic and can thereby present myself to the general public as having a job that is vague but not delusional. Win! I also like describing myself word because it is informative. It tells you something about how I work and how I process.
However, it's worth being careful not to harden one's sense of self too much around labels. As an intuitive, I can use rational processes and I have lots of emotions. Sometimes reason or emotion is the best tool for the job. To be the best intuitive I can be I want to know when that is and use the process that is best suited to the situation.
Being "An Intuitive" really just means that you use intuitive processes in your work or that you have a preference for using intuitive processes. You might be an intuitive by vocation or simply because you love making decisions intuitively, but in each case, we are really talking about using a specific process or set of processes. It's not that people are actually divided into two separate categories of "intuitive." and "non-intuitives." Everyone has access to the different faculties.
One reason that it's really appealing to identify as an intuitive is that it can give us a sense of value. Intuitives can be kind of ignored and undervalued by mainstream society and it's great to create communities and identify with our strengths. Identifying as an intuitive can make us feel more free to function in ways that feel natural to us, within the context of a society that tends to privilege rationality and sensory information. This is helpful.
It's less helpful to reject our less dominant processes and, for example, refuse to use a rational process when it's the best one for the job at hand. It's also not helpful to identify our selves as being in opposition to other processes.
This is why I advocate for integrated processing. I teach people to work with their intuition, but I'm really teaching people how to move through the world using the right process for the task at hand. By flowing easily between our faculties, we become more able to flow with the world around us.