I studied, worked and lived at many countries, I am still living in abroad. So, I am used to be an "alien" since my early adulthood. I would say, at the very beginning I never thought cultural differences can be a huge issue. Even if you can speak language perfectly, if you don't know good enough about popular culture, history, literature, geography, religion, etc. , you wouldn't understand half of the jokes/gestures of your colleagues. Well, if you couldn't find a solution, you wouldn't be a part of the community or in worst case you will be isolated and surely fail all your targets. I have my experiences and now I became a master for this game. So, I can understand T'Pol's attitude mostly and she is definitely not arrogant for me, her cultural codes are different than the community.
At Broken Bow almost every character is more agitated/aggressive/out of the role than the personalities that we learn at next four seasons. For a pilot episode which is very understandable. Nevertheless, I never get fully, why T'Pol stayed with those bunch of disrespectful, bigheaded space amateurs.
I wish Hoshi's character development was better written. Why should Hoshi must be so weak, so anxious, so girlie girl? She has an academic career, multicultural experiences and we we learnt at the very end, she is not an innocent baby. Why should she act/feel so insecure so long time?
Well it's true isn't it, there's T'Pol constantly provoking Hoshij for.. what reason? Attention.
Maybe she was upset from Hoshi's under performance, unprofessional reactions like me?

(Well, someone who works in men dominated business, who has to be muuuuuch more better than random male to get the same position, I can totally follow her reactions. I have to admit, as a mentor I am more skeptic about the works of junior female engineers, I know how hard will be their path to success.)
At the ENT Bible they planed for both characters a sister-like relation, why TPTB gave up this idea? Instead of stories done before they should gave us a Hoshi/T'Pol episode.
