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Desync
Not FPS
Short answer
The body you shot was already around the corner. Ping is not a skill issue until you've read this.
Also: desync · rubberband · lag
How it works
Desync is the server and your client disagreeing. Rubber-banding, delayed doors, ghost shots.
What to do
If the duo is rubber-banding, don't take the fight. Relog is a tool, not a shame.
Don't
Don't invent a ping number that fixes it.