Vulcans use “logic” to disguise their emotional attachments frequently in the show. They claim something is logical when it’s a purely emotional situation and logic doesn’t really apply. Not that Tuvok personally has those tendencies.
Tuvok’s character arc heavily involves him realizing that he’s got to have a little bit more of an understanding of emotions in other species, since he is third in command and Voyager will be without support for years if not decades. He’s showing empathy but only stating facts, his child is in a similar situation and Ensign Wildman has done a good job in raising Naomi. He knows hope is important to her ability to function in the situation and he alleviates her concerns as quickly as he can merely by pointing out the truth and explaining to her why she shouldn’t fear the outcome.
He’s developing his leadership skills as it pertains to other species, not just the leadership that works with Vulcans.