Prove what?
That I'll tear you to shreds? Ok, here we go:
You spent the first 30 seconds establishing that you're biased and everything you say has to be taken into context.
"Aegislash is simply unlike anything [you've] ever seen." What kind of lame reason to ban something is that? A pokemon evolving in battle for new typing and better stats has never been seen before, but nobody's stupid enough to try to ban that.
You said that "effective BST of 720" line, and that is a huge red flag to me that the person hasn't read a single page of this thread, and hasn't put a lot of critical thought into this. It has that for 1 turn, after, it has a BST of 520, with amazing power but terrible speed, so to avoid getting outsped by almost the entire tier and taking huge damage, it has to either use a low base power priority move, or it has to give its opponent a chance to boost up, heal up, or inflict some status on it. Best case scenario in a lot of cases is to stall out that turn by absorbing an attack. It's way too much to expect them to go for a contact move.
You said it had godly typing, but if this thread has done anything, it's shown how common and easy to fit on teams pokes that can check this mon are. Despite that sky-high SpA, he gives plenty of switch in opportunities for pokes that want to switch in and spam EQ or flamethrower or any other effective non-contact move.
You mentioned it having Deoxys-N offenses, but without that speed and relying on comparatively low base power moves like sacred sword for coverage, it's offenses are easily more comparable to standard offensive pokemon, but they all either have speed capable of abusing them without relying on a highly abusable move like KS, or consistent defenses that don't leave you completely vulnerable if you fail to KO.
You made a big deal out of it making certain pokemon less viable, and a lot of people have pretended this is a damning argument, but it'll be true of any top threat! Keldeo is a lot less viable than it was last gen largely because of Venusaur. Heracross got a mega, but can't be used much as long as Talonflame exists. In past gens, dozens of pokemon were made irrelavent by stealth rocks, and we didn't ban that. If other pokemon potentially being broken doesn't work as a reason to keep it, then other pokemon being made more viable isn't a reason to get rid of it.
Your claim that things run coverage moves like EQ just for it has been the topic of much debate, and if you had paid ANY attention to this thread, you wouldn't have posted such a callous statement about it without going into your justification for it immediately after. Basically, a lot of pokes carry coverage for it, yes, but not just for it at all. Most pokes that carry EQ coverage also need to deal with Heatran. Most that run fire coverage also want to hit Ferrothorn. Most that run dark coverage do it because dark moves are SO good right now (knock off and sucker punch?). And you explained that ghost is a great attacking type, so if you can, why wouldn't you run it?
You said "I don't understand" a lot. You clearly don't. If you really are a good player on showdown, good for you, but quit trying to make arguments if you're clearly not willing to read or listen to opposition. I've said it before, it's on the pro-ban side to "prove it", all I have to do is show how you're biased or incorrect, and you are clearly both.
This isn't a clear cut suspect test. I don't mind people disagreeing with me if they explain their reasoning. Heck, I might even vote for a ban (seems unlikely after my suspect testing experience, but that might just be because I really dislike simulators with their lag and weird aesthetics), but I'll state my observations as I see them and amend them as I'm proven incorrect, how about others do the same, or at least be honest about how you're voting for your own personal reasons.