There is a struggle between you involving the work that your lover does and the way that you feel about it. Maybe their career takes a lot of their time and attention, which they might otherwise spend on the relationship -- which could hurt your feelings. A workaholic plus an oversensitive homebody doesn't make the world's greatest couple, and this is just the type of emotional struggle you're involved in together.
You start to notice a tension that springs up every time that button is pushed -- your lover talks about their work or mentions needing to go out of town on a business trip, say, and you just clam up, unreasonably hurt by this news. Unfortunately, if you want things to work, much of the adjustment has to be on your part; you have to grow accustomed to the very things that hurt your feelings. Posing an ultimatum -- 'It's me or your career!' -- is unfair, and might not have the effect you hope for. A little insecurity might just be a necessary byproduct of the relationship. If you're able to talk about these things together and keep checking in with each other on your feelings about everything, you can actually come through the experience stronger, especially if you're able to learn to rely more on yourself for emotional sustenance than on your lover.