Scenario: Rogue is hidden and sneaks up on a Wizard. Rogue attacks and hits the wizard with 1 above his AC. Can the wizard take his reaction to Shield from it?
Shield's casting time is 1 reaction, which you take when you are
hit by an attack or targeted by the Magic Missile spell.
Until the start of your next turn, you have a +5 bonus to AC, including against the triggering attack, and you take no damage from magic missile."
The wizard is arguing that the RAW is any attack that hits him. The Rogue is stating that he's hidden and that the wizard shouldn't be able to see it coming. To this the wizard argues that when you attack you lose your stealth and gives enough time to activate a reaction.
Best Answer
You've already stated the key point:
So what you need to understand here is that the Shield spell involves time travel. No, really, it does. You can cast Shield when you're hit by an attack. Not when you're targeted, or when someone tries to attack you, but when you're hit.
The time travel shenanigans comes into play because the AC bonus of Shield applies to the attack that caused you to cast it. So stealth doesn't apply here, because when the Rogue stabbed the Wizard, it gave away his position. Then the Wizard changed history with the Shield spell.
See here for a similar explanation phrased a little differently. It's easy to understand how this works in terms of gameplay: wizard gets hit, wizard casts Shield, wizard does or doesn't get hit based on his new AC including Shield. How it works in-game is, well, magic! (Alternatively, if you prefer, A Wizard Did It.)