Well, essentially everybody has emotions unless you don't really care about the outcome of a discussion. Expressing those emotions is often considered unprofessional. Nevertheless, most people act in conformance with their emotions (even if they don't express them). So in fact, not talking about the emotional state would be insincere (as it exists and affects what everybody is doing).

Articulating your own emotional state gives the other person a better chance to evaluate your perspective. Furthermore, even if it might look like you don't really care about the topic as you act detached, you can show that you have rather strong feelings too, but keep them in control to stay constructive and professional.