Identifying spell effects currently affecting an item/creature or spell origins of an item, learning the number of charges of a magic item, and dramatically reducing the time expense.
You can use the identify spell to identify any spell effects an item or creature is currently being affected by or the spell used to create an item (see the spell description from the SRD or PHB).
You learn whether any spells are affecting the item [you touch throughout the casting] and what they are. If the item was created by a spell, you learn which spell created it.
If you instead touch a creature throughout the casting, you learn what spells, if any, are currently affecting it.
The short rest option for identifying the behavior of magic items does not replicate the options above, since the short rest option only applies to magic items (and, depending on how the rules are interpreted, maybe even only those that require attunement).
In addition, you learn how many charges a magic item has.
If [the item you touch throughout the casting] is a magic item or some other magic-imbued object, you learn its properties and how to use them, whether it requires attunement to use, and how many charges it has, if any.
The short rest option makes no mention of learning the number of charges, although it is common for a DM to rule otherwise (see the description of this activity in the Magic Items, Attunement section of the rules from the SRD or DMG).
[A]t the end of the short rest, the creature gains an intuitive understanding of how to activate any magical properties of the item, including any necessary command words.
Finally, the above advantages are in addition to the reduced expense of time. In order to use the short rest option to learn a magic item's properties and also become attuned to it, you actually have to spend 1 short rest learning its properties and then another becoming attuned.
Attuning to an item requires a creature to spend a short rest focused on only that item while being in physical contact with it (this can't be the same short rest used to learn the item's properties).
That's a total of 1 hour of resting to learn some of its properties (or 2 hours if you also want to become attuned), as opposed to a 1 minute casting time to learn all of its properties (or 1 hour and 1 minute if you also want to become attuned). Since identify is a ritual, it can also be cast in 11 minutes without expending a spell slot.
The answers are in your quotes. Only the last sentence about attunement refers to the voluntary process:
A creature can also voluntarily end attunement by spending another Short Rest focused on the item, unless the item is cursed.
This is reinforced by the sentence under cursed items:
Attunement to a cursed item can't be ended voluntarily unless the curse is broken 1st such as with the Remove Curse spell.
Neither of those affect the forms of ending attunement involuntarily:
A creature's attunement to an item ends if the creature no longer satisfies the Prerequisites for attunement, if the item has been more than 100 feet away for at least 24 hours, if the creature dies, or if another creature attunes to the item.
So in this case, Player B can indeed attune to the item if he can get his hands on it, and this does (involuntarily) end the attunement to the item of Player A.
Best Answer
The Shield of Missile Attraction does not automatically attune to characters who use it. Attuning to it causes its "curse" to kick in, but it has no ability to automatically attune or force its wielder to attune. The point you might be missing is that unless you attune to it, you also don't get the resistance to ranged weapon attacks.
The resistance to ranged weapon attacks is a magical property, and the Shield of Missile Attraction includes the "(requires attunement)" tag, so you don't get the "curse" or the benefit unless you attune.
You may have noticed that I put scare quotes around "curse". Yeah, that's an important point here. The shield grants you resistance to all ranged weapon attacks, so causing them to hit you instead of your allies isn't really a curse - it's the greatest benefit the shield has to offer.