Living in a busy house with children, I am no stranger to arguments. And, as a frequent observer of these debates, something I’ve noticed is that it is always helpful when the other side makes your own argument for you.

Something like that happened in the investment world this week, and it’s worth noting because there’s a great lesson in it for individual investors.

First, a little background: you may be familiar with the ongoing debate in the investment industry between supporters of so-called “active” and “passive” funds. In short, the debate boils down to this question: is it worth the money to pay a professional (a lot) to pick stocks for a mutual fund, or would the fund be better off by dispensing with the stock-picker altogether and simply buying a list of stocks to hold for the long term?

The data on this question has been very clear: over the years, passive, or index, funds have delivered demonstrably better performance than active funds — that is, those run by human (and highly paid) stock-pickers. There are at least two reasons for this: First, human stock-pickers are prone to making mistakes. And second, even when they get it right, human stock-pickers’ sizable paychecks often outweigh any benefit they provide.

Sometimes this debate seems a little shrill, with both sides talking past each other. This week, however, a curious thing happened: one of stock-picking’s most prominent advocates, the billionaire hedge fund manager Leon Cooperman, inadvertently offered a perfect example of why index funds are the better choice for individual investors like you and me.

In an interview on CNBC, Cooperman provided a vigorous defense of hedge funds, and active management in general, which have delivered subpar performance over the past ten years. The arguments weren’t altogether unreasonable, but the interesting part came right at the tail end of the interview.

The interviewer asked Cooperman about his fund’s holdings in Apple stock, which has done terrifically well over the past year. Cooperman’s response was candid: “We mishandled Apple…We out-traded ourselves. We had it and we got out prematurely because we were concerned about competition, but we were wrong.”

No doubt, Cooperman is highly skilled, with a talented staff and decades of wisdom and experience. And yet, here he was acknowledging that he “mishandled” Apple, the biggest and one of the most popular companies in America.

Here’s the conclusion I draw from this: If someone like Cooperman is susceptible to missteps like this, then certainly the rest of us are too. Yes, there will always be the Warren Buffetts of the world, people who demonstrate outstanding stock-picking skill over a lifetime, but that’s like saying there will always be Babe Ruths. Sure, they exist, but there are very few of them, they are very hard to find, and even if you do find one, their funds invariably are closed to ordinary investors.

For that reason, I believe the best choice for investors is to avoid “out-trading” yourself. Heed Cooperman’s (inadvertent) warning: go with simple, low-cost index funds to give yourself the best shot at achieving your financial goals in life.

P.S. If you’re interested in this topic, you can find Coooperman’s interview here, you can find current hedge fund performance data here, and you can find a fantastic video explaining index funds here.