In the mood to Make Lists
Reasons the Master doms, even though they're a sub:
Because it's a skill they've gotten good at, and it feels nice to be good at something
There's an element of "service domming" when they do it to the Doctor. In that they know the Doctor seeks out people and situations that hurt them, they know it's a reliable way to keep the Doctor's attention, they know the Doctor "wants" to be punished/to not be the one in control (airquotes because the Doctor's relationship to subbing is similarly complicated. Which could be its own post)
Insecurity. Control freak-ism. Making a point that they're not "weak" like their society (slash the Doctor) expects them to be. Shame about their real desires, and the idea that their submissiveness reveals their True Inferiority. Reenacting their own traumas but as The One Doing The Hurting this time. Trying to position themself at the top of the social hierarchy by way of the sexual hierarchy. This is more of a factor with, ex, Spymaster (particularly insecure about being the Doctor's biological inferior), and less of a factor with, ex, Missy (more comfortable with herself. And also she's sexist, so she feels more "allowed" to embrace being a sub as a woman)
When domming non-time lords: time lord supremacy is pretty inextricable from the whole thing. It's about working through their anxieties about whether they're Really superior or not. There's also probaby an extent to which they feel like that's the Only role they're allowed to take with a human (although they still push the bounds of that. by engineering scenarios where unit will drug and restrain them, etc)
Treat Others The Way You Want To Be Treated :). The Master would actually quite like to be murdered sexual style, so they do other people the favor of delivering that experience (this is particularly central to, ex, the Osgood scene). And then they resent the Doctor for not returning the favor (while never communicating that they want the favor returned. Or that evil-scheme-domming is a Chore they do with the expectation of Reward)
Domming is legitimately kind of fun and sexy to them. But like, in a funny haha way. A flirty foreplay way. Not really the main event. Not the kind of intrinsic/instinctual desire that Really takes the knees out from under them
Bratting. They dom in the hope that you'll eventually get frustrated enough to Teach Them A Lesson and take over as the real dom
Legitimately really mad at the Doctor for various Wrongs committed against them, but trying to channel that anger into Fun and Sexy outlets ("I should shoot you in a jealous rage. Now wouldn't that be sexy?") Believe it or not, I think they approach evil-scheme-domming as the healthier alternative to Real Revenge (and they don't think of what they're doing as Real Revenge like 90% of the time). Cloaking their hurt in a lot of irony and performance and playfulness also makes them feel less vulnerable
Incurable theater kid. If they're going to be killing people anyway (for reasons too lengthy to get into here), then they might as well make an elaborate game and performance out of it. And there happens to be a handy template for that -
Always funny to see the Doctor get caught on the wrong foot or do some manner of looney tunes pratfall. "Suits you, flustered, it's a good look, you should try it more often."
They've really committed to the bit of being The Bad Guy. And dom/sadist is the Bad Person role :) (which is why it's so delicious to know that's what the Doctor really wants but won't allow themself)