You played well but 4...Bd6 is such a crap move that any reasonable response by white gives winning chances. Check out a database and notice that 0-0, Nc3, dxe5, Bg5, d5, Ng5, and Qe2 all work. Still, I enjoyed your analysis.
A position in the Italian
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Many people like to reach this position with black when the italian is played:
And many players are having a problem playing against this because they are afraid of black pinning their knight to the king, so they prefer not to bring the knight out.
Today I'll show you that you got nothing to be scared of. An opponent played this setup to pin and attack my knight and I discovered a way to destroy it: