Whilst he obviously has specific Dark Side related reasons for starting to wear the mask, since he and Hux started to get closer Kylo has become increasingly reluctant to ever take it off in public...because he feels awfully plain and awkward compared to his famously beautiful partner.

Everyone seems to make a big deal about Hux's perfect bone structure and his flawless skin and his gorgeous flame red hair, they make comments along the lines of Kylo being the brawn while Hux is both the brains and the beauty, he has suitors fawning all over him at official functions, and even his detractors seem to use 'pretty boy' as their go to insult. Kylo's left afraid that if people were to see what he really looked like everyone would start wondering what in the galaxy Hux was doing with someone so comparatively unattractive.

Cue Hux reassuring him that he has nothing whatsoever to be insecure about...

(Bonus points for Hux pointing out that people probably assume he's the better looking one because Kylo keeps hiding under the mask)