English Rat Defense: Clawing back

Last night while sitting at home I heard a minor commotion outside my bedroom window like a neighbor was clearing out storage. When I left the house in the morning there was a package of sliced turkey on the stairs. A cat must have been struggling to tear it open and get at the meat inside. I debated if I should bother throwing the package out or leave it for the cats, and ultimately decided on the latter. On the way to work, however, it occurred to me the meat might attract sewer rats.

In this morning's game Lichess matched me against one arcolombo698, rated 1665 out of the U.S. Lichess classifies the opening he played against me as the Rat Defense: English Variation. Unfamiliar as it was to me, I couldn't tell if opponent knew what he was doing or was trolling. He knew what he was doing -- but that is the kind of opening the Rat is. When Black loses castling rights on move four, White can't help feeling he's gained an advantage, and that makes the ensuing feeling of being stuck all the more frustrating.

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Position 1: White to move

Assigned the white pieces I opened 1.d4 and after 1...d6 continued 2.c4. Black pushed 2...e5, and this is officially the English Rat. I exchanged pawns and queens with 3.dxe5 dxe5 4.Qxd8+ Kxd8. With Black having lost castling rights and me being a move ahead, one would think the eval bar would favor my position -- but no, and after 5.Nf3 I was down to -0.2. It turns out the engine wanted 2.Nf3.

Black defended e5 with 5...f6, and I continued 6.Nc3. Black pushed 6...c6, and I pushed 7.e4. Black and I developed with 7...Be6 8.Be3, and Black correctly played 8...Kc7. With Black's king awkwardly positioned on the queenside, a pawn storm there seemed like a sensible plan. The engine disagreed and 9.a4 increased Black's advantage from -0.2 to -0.9. It got worse, though. Black correctly replied 9...a5, I developed my bish with 10.Be2 to prep kingside castles, and after 10...Nd7 and 11.0-0 Black's advantage grew to -1.7. What the engine wanted was 11.0-0-0, which seems absurd given how porous the queenside was and how safe the king looked on g1.

1. Why did I choose the move 13.Rd2?
2. Why is my move not ideal?
3. Why is the better move better than my chosen move?

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