No its not, but how do you account for feeling about something that goes against your logic? Ie quitting a job without finding another. How is emotion guiding logic in every case?
Emotions motivate you to act to improve your situation instead of do nothing. They may be illogical, but they kickstart the thinking process. Logic is useless if you don't wake up and use it. Emotions are the first past filter to bring issues to your attention.
The emotion doesn't tell you 'quit without finding another job' it says "I don't like this" which prompts you to use your logic to change your environment.
One logical statement doesn't have to support another logical statement. We wouldn't be able to get logical paradoxes such as the Paradox of the Court without conflicts in logic...
With regards to quitting a job without finding another, taken rationally you could argue that the individual has decided that in order to have the positive outlook required to land a new job they need to remove themselves from a negative environment they find themselves in. Such an outlook is logical, it recognises that emotional state has a large impact on confidence, and that confidence is a very useful attribute for landing a new job. Of course it could also be much simpler than that, that the individual just wants to improve their emotional state in the short term, not all logic has to apply eternally.
That's just a basic example. A more complex example is what we understand by 'truth'. To me, we know when something is true because we feel it, or in other words truth has an emotional response. Is that your experience also?