>>3388730>>3388754It doesn't matter how good you are because she saw Shinji first, and she probably likes Shinji partly because he's a dork.
In fact, when the dandy megagay Kaworu turned up Rei was suspicious of him. You might argue that Rei simply dislikes homofaggots but since Rei also hates Asuka within seconds of meeting her for being an imperious bitch we can treat this as collaborative evidence that Rei doesn't like people who are too big for their boots.
The way to Rei's heart is making her miso soup and cleaning her fucking apartment. Rei also likes being complimented for scrubbing the floor well. Your first mistake was to assume Rei would be more interested in your qualities as a chiselled masculine specimen and not your ability to cook her some poka poka-inducing soup, because what she wants is the frickin' soup.