Aegislash's simultaneous offensive and defensive capabilities are unmatched in OU. With its pseudo-base 720 BST, it contributes to teams in incredible ways even with minimal investment and planning. Aegislash's offensive power and incredible Ghost-type STAB coupled with its coverage options make it next to impossible to reliably answer. Dark and Normal-types fail to reliably respond due to Aegislash's coverage options, and Pokemon heavily invested in special defenses typically lose to coverage. Aegislash has an array of viable options at its choosing, allowing an Aegislash user to pick and choose how the enemy will handle Aegislash prior to the start of the game. All the while Aegislash is capable of running a very threatening Substitute + Toxic set, punishing teams relying on passive Pokemon such as Mandibuzz, Mantine, and Hippowdon, while also giving Aegislash more security behind a Substitute. Substitute allows Aegislash to avoid status, potential Scald burns, as well giving Blade form more room to spam attacks. Aegislash can even provide teams with reliable Pursuit trapping, allowing it to trap Pokemon such as Latios and Tapu Lele.
Aegislash is so flexible with what it can do, and different sets beat different things, making it easy to lose simply because you thought it was a different set. It can set up with Swords Dance, it can use Substitute to avoid status and take hits it otherwise wouldn't be able to, it can stall with Toxic, and more.
Aegislash's movepool, stats, and ability alone make it an absurd force in the metagame, but couple it with its typing and it is over the top. King's Shield is an incredible move, not only presenting Aegislash the ability to give convert to Shield form and give itself incredible defenses, but also the fact it presents the game with more straight up 50/50 opportunities. While Pokemon is all about prediction and it might seem as simple as a guessing game, a straight up 50/50 does not reward based off of skill, but rather who won the coin flip. Consider this situation: You have Aegislash, in Blade form, out 75% vs your opponent's Swords Dance + Life Orb Weavile. These are the only two Pokemon remaining. You have the option of using King's Shield on the predicted Knock Off, which would otherwise KO your Aegislash and lose you the game, or to attack on the predicted Swords Dance, which would lose you the game should you King's Shield. In this scenario, the winner is not determined by anything skill based, but simply a guessing game. King's Shield even grants it the immunity to being reliably Pursuit trapped by Dark-types, as the only Pokemon that can really trap it is Bisharp, which fails to OHKO max HP Aegislash with Knock Off if Jolly, while Adamant Bisharp can potentially be outsped and OHKOd by max speed Sacred Sword Aegislash.
Not only sporting essentially 60/150/150/150/150/60 stats, it also has an incredible typing and a move that invalidates any physical attacker. With the many sets it can run and incredible defenses, if you predict the wrong set, you pretty much lose the game.
TL;DR, Aegislash's incredible stats, a great typing, amazing versatility, and a game-defining move in King's Shield made it too powerful for the metagame.
However, in Gen 8 it was nerfed, giving it worse stats and making King's Shield less powerful which is why it wasn't banned in Gen 8.
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