In a history class at DePauw years ago, a professor asked us why we study history. The students answered with the obligatory "Those who do not learn the lessons of history are destined to repeat them" line, and she shot that down. I forget what exactly she said. Her point may have been that historical contexts are unique, and so what works or doesn't work in those cases is irrelevant to what works or doesn't work now. There were so many factors in specific historical contexts that are not present now, and people may also have been different from us, so how can we say that the past can instruct us?
Personally, I don't toss out the "Those who do not learn the lessons of history" cliche, as happy as I was that my professors shot down those who thought they were being so smart by repeating it. Some things do consistently work or don't work, whatever context you may look at. People are different in various historical contexts, but there are some things in human nature that remain constant (e.g., greed, lust, some altruism, etc.).
But here's my professor's answer for why we should study history: because it is so fun! Yes it is, even though I've often struggled in college-level history classes.