I would typically say this in English as "How could you have missed the train?", since we're almost certainly discussing this after the incident has happened. Would it be unusual to say "Hur kunde du ha missat tåget?!"?
Yes, very. The key difference here, I think, is that English emphasises treating the event of missing the train as something that has happened in the past, while Swedish emphasises the state of having missed the train, which is still ongoing. You could very well say "hur kan du ha missat tåget?!" and it wouldn't be odd, albeit a tad less common. For "kunde" to be normal, you would have to discuss a state of having missed the train which is no longer relevant, for instance if you talk about "that time five years ago when I missed the train" or similar. But even then, "hur kunde du?" would feel more natural. We love past tense.
I'm still a bit confused here. Why is missa in the infinitive? Is that a normal Swedish thing, to only preterite one verb, and not both?
Yes, and it is in English too: Han kunde läsa 'He could read', Vi har kunnat äta 'We have been able to eat' etc etc etc. The norm is that only one verb inflects for time. In both languages.
Interesting. Thanks. "How can you have missed the train?" sounds very strange to me in English. For some reason, we feel the need to put both verbs in the past, even when it would seem more logical to say things like "How can you have done that?" (meaning how can you now justify having done that?)
Oh yes, it feels completely off to me as well in English, and I'm not even a native speaker. Funny how the differences can be so large at times, even when the basic grammatical functions are essentially the same and the languages are related.