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I dont see why white plays d4 ?
Damn good question!
Your chess instinct, intuition is dead on target. It is true that White gets a nicely centralized knight on d4. And a temporary lead in development. But he does this at the cost of an essentially permanent advantage for Black. That advantage is that now Black has 2 central pawns at (e7 and d6) vs. White's 1 central pawn at e4.
This 2 pawns vs. 1 pawn advantage for Black in the center is but one factor of many that are important in the position after 1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4