They argue all the time. They have been doing this since the beginning of the mission. The tension was obvious. People were actually betting on when her boyfriend would strangle the captain again. (Crewmembers are also making other wagers that she's not supposed to know about, but does anyway.)
How can a First Officer truly do his job if he is always fighting with his Captain? Apparently quite well considering the two had the highest efficiency rating in the entire fleet. They work so seamlessly together after only a few short months it seems as if they could read each other’s minds. Yet the moment the mission is over there at each other's throats. At least this time it's only in the figurative sense. (If she hears Ensign Thompson say one more thing about erotic asphyxiation in relation to the "bridge incident", she is going to strangle Brittany herself and there won't be anything sexual about it.)
At first, she wondered why Spock even took this job. It was obvious that her boyfriend did not get along with Captain Kirk. Maybe it was because of her. In her heart, she likes to believe that was the reason. In her mind, she knows her theory is illogical at best. Her boyfriend tried to be the epitome of logic therefore he would not make any career decision based on romantic feelings in relation to her.
The little girl inside of her who believed in fairy tales wants to believe that he loves her so much that he would be willing to put up with a complete ass of a boss just to be near her. The Starfleet officer that she has become wonders after everything if he is even capable of loving her at all.
Before the destruction of Vulcan he never once said the words ‘I love you’ to her. Now she wondered if it would be possible to ever hear the words from his lips. Between losing his mother and a lifetime of being conditioned to suppress all emotions, she wondered if he would be able to say those words to anyone. She wondered if he could express any feelings at all to anyone at this point. Though she loved him as he is, she needed some outward indication that he cared. The way he kissed her did not count.
Yet there was one person that could get an emotional response from her boyfriend. She knew that person made him feel things that he wasn't ready to acknowledge. At first, she thought her boyfriend only felt hate in relation to his captain. Yet as time went on, she realized it was a completely different feeling. It was obvious to her that the captain triggered an emotional response in her overly logical boyfriend that no one else could, not even her.
At some point, she realizes that Jim and Spock were not actually arguing with each other. What she perceived as arguing was just a very passionate discussion. Her boyfriend's use of the Vulcan equivalent of yelling was just how they talked things out. (Not that Vulcan's actually yell, instead her boyfriend just raised his voice slightly with an angry eyebrow raised in relation to their captain.) It was speaking with passion and as a communications expert she realized what that really meant. At that same moment, she became aware that she could never get that type of emotional response out of him.
When he was around her it was all about logic and doing what is most prudent. He never allowed his emotions to show in front of her. He hasn't cried once since his mother died (or at the very least not in front of her). He never tells her that he loves her. The most she ever hears is "I find your company mentally stimulating."
When he is around the captain, his logic begins to slip a little. When she watches him with Kirk, she can see this passion in him that is absent when he's with her. On the surface that passion seemed related to hate, but she knew better. There is an old saying on earth about love and hate being two sides of the same coin.
She doesn't know what to do with this knowledge. She decides to do nothing and let the relationship between her and Spock stay as it is. If he does not realize what's going on she will not enlighten him. It's the only logical thing to do. Her boyfriend will appreciate her logical decision.