I'm guessing because it sounds like only a part of the sentence. It would sound better if there was a temporal adverb(ial), for example "my cousin was still alive last week/last year/two years ago/when that happened". This way it sounds a bit incomplete because it's in past simple, which usually goes with a particular time in the past, which may be explicitly stated, or implicit in the context.
This course does a good job of teaching us sentences that fit just fine during a conversation. Yeah they could have given us a longer sentence that has more context, but once we're going to be familiar enough with Swedish to be having full on conversations, shorter sentences like this will be much more common and we don't have to relearn how to be less formal/long winded once we're at that level. That's a pro of this course over a traditional class.