Giving this to a player like: [insert troll face here]

One thing I enjoy thinking about is how to to make constructive use of Cursed items... 

For instance, imagine a Sharpshooting Battlemaster/ rogue wearing this Resistant to Piercing armor who can move 1/2 their movement as a reaction if someone enters their melee range.  This makes them twice as tough as long as they're mobile... And there are plenty of ways to maintain their mobility.

Or just moving this curse onto Leather Armor or a Breastplate...

Or Resistant to Slashing Armor on a knight or Paladin who carries a cursed Arrow Catching Shield but can also cast Shield as a Reaction.  Now, she's got a great armor class and is in a good situation in most cities.  Its only against bludgeoning weapons from barbarian hordes that she'll have a problem...🙂

lied to a player told him it was a armor of invulnerability. 

Okay, so maybe Im just crazy from reading the descriptions for too long. But the description here says you are resistant to 1 of the 3 types of physical damage.

IT DOES NOT SPECIFY only nonmagical damage, as does its big brother the Armor of Invulnerability, which means that the resistance DOES apply to magical Bludgeoning, Piercing, or Slashing damage as well.

So inherently if you have 2 party tanks, 1 wearing this armor, and the other with the Interception or Protection fighting style you can cheese the vulnerability system.

Again, if you really want to break the universe, you can pull a little combo i like to call the bullet sponge.

Fighter lvl 1, monk 3 (for fighting style, defense +1Ac, Shield and Heavy Armor Proficiency, and Monk's Deflect Arrows.)

Take the shield of missile attraction, get cursed so any ranged attack targeted within 10ft of you instead hits you, then drop the shield and switch out for the Shield of Arrow Catching raising base Ac to 21, 23 against ranged attacks. Then don the armor of Piercing Vulnerability and attune for 1/2 damage from all arrow and bolt attacks that do manage to hit your impossible Ac, and 2x damage for sling stones/boulders.

When such a sling stone/boulder does inevitably fly your way, use your reaction Deflect arrows if it manages to hit to reduce damage you take and potentially catch and return the attack.

I thought Identify did not Identify curses? Otherwise what's the point of having cursed items?

Typically that is the case. This is a specific exception to the rule about Identify not detecting curses. Specific rules trump general rules.

Since the phrasing for remove curse is "At your touch, all curses affecting one creature or object end. If the object is a cursed magic item, its curse remains, but the spell breaks its owner’s attunement", and the curse says "Attuning to the armor curses you," couldn't you target the player character with remove curse and use the armor without any negatives as long as they don't reattune to the cursed item?

magic objects that reguire attunment act like a nonmagical object when not attuned since remove curses unattuntes you you get rid of curse but also resistance 

Can you have a body part chopped off while wearing it?