The only hope of solving this issue is to temporarily stop struggling with each other over the overt issue (will he or won't he join). Since you are both on completely opposite sides of the fence, if you continue to wrangle on the issue, you will become more and more polarized until you end up in a deadlock.
So for now, let's put the decision aside and work for insight. Your husband needs to understand that a person's career choice is usually driven by unconscious motivations. More specifically, career choices are often motivated by the wish to heal childhood wounds. For example, a boy who was battered by an abusive father may become a boxer who beats up others, thereby rewriting his history so that he is on top instead of the powerless victim.
The fact that your husband is so welded to the wish to join the FBI makes me suspect that he, too, is trying to right some wrong from his past. If I am right, his urge to rewrite his history is purely unconscious, as is his urgent need to join the FBI. If we can help him to become conscious of why he feels such a burning need to join, there is a good chance that he will feel liberated from the need.
In order to help him become conscious of what unfinished business is spurning him on, you might ask him what needs he thinks will be satisfied if he joins the FBI. Ask him if he can find a link between his burning desire to join and unfinished childhood business. If he can find the link between his unfinished business and the desire to join, he should also be able to see that catching bad guys will not alter his past. The only way to heal the wounds that stem from his past is to access his feelings and work them througH.
He needs also to realize that his drive to join the bureau is what we call an enactment (when a person goes into action in order to solve an emotional issue). Recognizing the root cause of his need to join the bureau and talking about the memories and feelings that have created this need is his only true hope of healing. Enactments never heal the problem; they simply keep a person stuck chasing his own tail.
If you can't make headway on your own, then go to a marriage counsellor. If and when you go to therapy, don't fall into the trap of focusing on the overt issue (will he or won't he join). Make sure that he talks about his history. And, while you are on the subject you might also ask him if he is willing to allow his vendetta to jeopardize the marriage?
Meanwhile, you might also try to understand how his wish to join reactivates your own abuse issues. Since you felt abused as a child, is it possible that your history is getting in the way? In other words, are you feeling personally wounded and victimized by his wish to join, when in reality his wish to join isn't about you at all but rather about his own wish to tame the demons inside himself? Are you translating his wish into proof that he doesn't love you enough? ('If he loved me, he wouldn't choose this career.')
Are you feeling that your needs and wishes aren't important to him (that you aren't first on his list)? If you could take your own wounded child out of this discussion, how would your discussions evolve? Would you feel more open to his following his career choice? Would he feel such a need to go if he felt that you were giving him the freedom to choose this path? How much of his need to join is being fueled by the feeling that he is being told that he can't?
If he felt that you were able to let go of the reins and let him go, would the need to join fade away? As you can see, both of you need to soul search and honestly listen and understand each other. When you are both clear on how your mutual histories are driving his choice of career as well as fueling your negative reaction to it, you will both be in a good position to solve the problem.
In this climate of insight and mutual understanding, you should be able to come up with a plan that embraces both your needs.