As I understand it, d3 is a better move than Re1 because the f file is guaranteed to open up and you're wasting a move "activating" when it will be activated in a few moves anyways. d3 defends e4, opens the scope of the c1 bishop and your rook will be opened up on the f file and may be able to connect with your knight on f7 eventually. Hope that helps.
Middlegame rook mistake
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Why is this considered a mistake? I placed my rook on a strong file, pinning the queen, which seems like a good move. However, after analyzing the position, it suggests that my opponent can respond with a sequence like Bc5, Kh1, Nf6, leading to complications.
I tried looking for alternatives to Re1, but almost every other move still allows the bishop and knight combo to check me. So why does it matter if my rook stays on the strong e-file?
One suggested move was d3, but even then, the opponent can still check me. What’s the difference?