The problem is simple, the mouse movement is very awkward (at least in my opinion), i couldn't have a good experience with the game because of that.

To fix this, you need to find a file named "AutoExec.con", it is located by default in "Windows (C:) > Program FIles (x86) > Steam > SteamApps > common > Star Wars Starfighter > Game " once you found it, open it with a text editor, you can use Notepad if you want.
Search the line "Call _MouseRotate, ReverseAxis2, On " and replace the "On" with "off", and add this line below "FlipMouseYAxis true, 1", it should look like this : (click on it to zoom if needed)

¡Enjoy!