Why did Coulson only start carving the Kree symbols after he saw Garret's carvings?
At first, it might seem that it was because his mind was erased, but the other T.A.H.I.T.I. patiants all had their minds erased and they still had the compulsion to carve, without, seemingly, seeing the symbols beforehand.
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when ward infiltrated that ukrainian site with glasses on and skye on comms, the glasses took a picture of that whiteboard in the room with those two guys doing calculations. there you can see those drawings for the first time.
even though coulson is on mission that time, it'd be important enough for him as the team leader to see whatever the enemy (probably garrett) wanted to get their hands on. that's why garrett started carving straight away when he got injected with GH325.
(Open invitation for someone to sum up)
Coulson was brought back to life in something called Project T.A.H.I.T.I., where a chemical called GH-325 was used to bring him back days after he died. His mind was wiped to erase the procedure. He later discovers that the chemical was from a dead Kree. Later, John Garrett, one of the show's S1 villains, uses a concoction made from multiple GH formulas to save his life, and begins carving the symbols you see in the image attached. At the end of S1, Coulson starts doing it too. It's like a compulsion, a bunch of things later, and they discover that it's a map to a Kree City, where one is supposed to use something called a Diviner, and when placed properly, it unleashes Terrigen crystals, which cause Inhuman powers.