Because he doesn't suppress his emotions very well.
He gets impatient, frustrated, sarcastic, and sometimes even makes a joke!
Tuvok is pretty cool for a Vulcan.
Actually, Tuvok is probably next to Spock my favorite Vulcan character, and I think he is my favorite Voyager character. I have always been impressed with Tim Russ's portrayal of Tuvok and personally think he is among the best actors who have ever played a Vulcan.
Though he seemingly does express frustration, usually due to Neelix, I actually think he suppresses his emotion quite well when you compare it to instances where his emotional suppression was not there (he is a very intensely emotional being then). Being middle aged for a Vulcan, a family man, and a former starfleet instructor, he is indeed well-rounded and well adjusted and IS what he IS and is OKAY with it.
It is a good contrast from other Vulcans we've seen because he is content to be exactly as he is: IE Spock being half human and constantly trying to suppress that side (not content with who he is and always striving to a certain extent to be something he isn't), Sarek actually being pretty emotional (disappointed yet loves Spock, marries a human, yet to an extent, is in denial about how emotional he really is), T'pol was very emotional (she was conflicted about her feelings for Trip and her mothers' disappointment in her: rumor has it she was supposed to be revealed as a Vulcan\Romulan hybrid~ too bad that never was to be). Though Data was an android, I'll include him because he was Vulcan like, and essentially the Vulcan stand in for TNG, yet was the reverse of Spock: perfectly emotionless, yet trying to be emotional. Again, Data is conflicted and not content with his status.
But not Tuvok. He was arguably an ideal Vulcan, able to retain his logic among so many emotional beings, but balanced it with being an effective and intregal part of the crew, knowing when he could "bend" his Vulcan principles on emotion, without breaking them. I especially liked the dynamic with Neelix. I always got the sense that his seemingly annoyance with Neelix, was really Tuvok's way of balancing being logical, with in some ways being a foil for Neelix to express his fondness for him and to show the crew he wasn't some emotionless, unapproachable machine, yet retaining his logical principles. I especially liked when Neelix departed Voyager, as a final good bye and acknowledgement to Neelix, Tuvok knowing if he really danced, it would be illogical and unseemly for a Vulcan to do. Yet did make a slight gesture with his foot, which was all Neelix needed to see, and for Neelix, spoke volumes to the depth of feeling and gratitude Tuvok really did have for him (Neelix and Tuvok helped each other over the years), but was unable to show publically and still be a "proper" Vulcan.
In fact, when a Vulcan is in the midst of a sea of emotional beings, wouldn't logic dictate that a Vulcan must, at times, balance Vulcan stoicism and logic, with finding small ways of being approachable and even congenial, if for no other reason than the logic of being an effective leader, to foster trust among crew mates, and to be able to relate to them. I tend to think this is a lesson he must have learned as an instructor, having to find different ways to relate and motivate his cadets\students.
So, yeah, I agree: Tuvok is a pretty cool Vulcan.