Suspension without my case legitimitaly being reviewed.

The reason for suspensions for short periods of time like that being ineligible for case reviews is because by the time the review is done the suspension would be over.

The thing is this with the suspension being so short it would not be eligible for a case review because by the time the review would be done the suspension would be over.

Every time someone reports you on Xbox Live, the console is gathering evidence and sends it in together with the report. All reports are checked by a real human being, so you aren't automatically (and unfairly) banned just because a group of people reported
you.

After the Enforcer reviewed the complaint and the evidence that came along with the report, they then decide if you should be banned or not.

The same goes with the Case Review. If you have actual proof that makes it evident, that your suspension was in error, you can send it in as a Case Review, and again a real human being will go over the case again, takes your evidence into consideration and
then either lifts the suspension, or if your Case Review brings no evidence that contradicts the original report, the suspension is being upheld.

So without knowing the exact details of your case, the only thing you can do is to use the "Case Review" feature, and to make sure your case review is waterproof (i.e. not some lame "I did only sent an insult back because that guy insulted me. Suspending
me for that is unfair!" or "I'm innocent, my brother/cousin/grandma was playing at that time").

Unfortunately without being able to submit a case review, all you can do is wait it out. Suspensions are not always issued the same day the action took place as investigations can take time.

So my account has got a 24 hour review after I swore at a guy for team killing me in Rainbow Six Siege and I can't apply for a review. The button is there but there I can't actually press it, Is there a way to fix this?

steeledwand7664 is correct. Suspensions lasting 24 hours dont qualify for a case review. The reason being is your suspension would be over before the case review would be finished.

That being said the case review is so people can dispute a suspension if they were suspended by mistake and didnt actually break the rules. Since you admit you swore at someone then you broke the rules so a case review likely would just get upheld and the
suspension would likely have stayed.