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Well it's all about the upgrades

It doesnt copy whether that creature is tapped or untapped, whether it has any counters on it or Auras and Equipment attached to it, or any non-copy effects that have changed its power, toughness, types, color, and so on

In this case, because your life total also can't change, that damage has any other effects that it may have aside from causing you to lose that much life (such as effects from lifelink or infect) and triggers and effects can see that damage was dealt even though your life total didn't change

That means any time any players creature dies, this cat is getting a significant buff