If there's 5 teams in your division, why is it unacceptable to win, on average, once every 5 years?
First, because that was considered a bright period in White Sox history. We could go back to 1960, the year after their last WS appearance (before the one they won of course), up to now. During that time, they only added an extra appearance in '83. 5 playoff births in 56 years, essentially one every 11 years, which is remarkably weak.
Because this was during a span in which both the Tigers and Royals were bottom dwellers for the most part. Tigers had zero playoff appearances from '88 until their 2006 WS birth. Kansas City went 30 years without a playoff appearance when they won it all in '15. So from 1990-2005, neither team was really competitive, so the Sox were in a race with Cleveland and Minnesota every year, and most years they fell short.
I never said the White Sox were alone, because there are teams that have had major struggles making the postseason. But I'm a White Sox fan, so I focus on them. I want them to be good, and they haven't been for a while now.