Is Tessa an arrogant character?
As much as I don’t particularly care for Tessa’s actions through a lot of the beginning of the series (novels/manga included), she’s more stubborn than arrogant. Though one could definitely say that she has been so many times before as a result of other things too. She was determined when she helped build the TDD-1, and when first starting to act as it’s commanding officer, I have no doubts that a lot of the time she had to fake her confidence in front of her crew.
Tessa and any of her arrogance seems to have been focused in two places: her pride in the security of the TDD-1, and with how she tended to treat the ‘competition’ between herself and Kaname for Sousuke’s affections. She fully believed that no matter what, the TDD-1 was hers to control. Gauron and his connection to Leonard destroyed that during their hijacking, though she was able to step back and admit that to save it, she herself couldn’t do anything. It *had* to be Kaname, because she was the better athelete, and would be able to make it to Lady Chapel.
As for Sousuke’s affections, it was shown mostly in how she acted when in direct contact with both Kaname and Sousuke. She made wild embellishments about spending time with him, and would make comments about how something about her would make her seem more desirable than Kaname, but when push came to shove and she was finally given an answer from him, she relented and moved on.
Tessa can be VERY arrogant if given the opportunity, but her saving grace is that when it came down to the reality of things, she was able to admit the truth to herself and move on from it. I have a ton of more respect for her from DVMC onward, but up until that point, admittedly, she got on my nerves a LOT!!