Something like "we're looking for someone with a different skill set" would still be reasonable honest, but also wouldn't make me feel terrible. The notion that you can fully asses someone's technical abilities from a one-hour interview is mistaken anyway. So an honest reply should take that in to account.
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A second scenario is where I did a take-home code test thinghy. I went for the "simple but obviously correct and easy to implement approach". The performance for that seemed more than enough for the stated use case, and included some benchmarks and a bit of text to justify it. Performance wasn't mentioned in the task, but seems like the common sense thing to do. After a few weeks I got a one-line "doesn't meet expected performance" rejection. Well, you didn't mention what the "expected performance" is motherfucker. That's not what I sent back (I didn't reply at all), but what a fucked up way to evaluate and dismiss people.