Why buy index funds when they are guaranteed to underperform their index?

Because the odds of that overperformance are low enough that your expected value will be less than the guaranteed underperformance.

The mere fact that overperformance is possible is not really meaningful; what matters is how likely it is. Taken to the extreme, it leads to ludicrous "justifications" of all manner of silly actions. Why would you ever not rob a bank when there is the possibility you might get rich and escape without being caught? Why would you ever go indoors when there is the possibility that at any moment a random person could see you standing on the sidewalk and decide to give you a million dollars? The answer is that in these cases the "overperformance" is very unlikely, so it makes no sense to act in a manner that takes account of the possibility of it happening.

Perhaps slightly less ridiculously, imagine a carnival game that works as follows. There is $200 cash sitting on the table. You have two options: take $100 and walk away; or, roll a die, and if you roll a 6, you get the whole $200, otherwise you get $50. Why would you ever take the "guaranteed underperformance" of $100 and leave money on the table when you have the chance to get the whole $200? Because it's better. If you take the first option your expected value is $100, obviously. If you take the second option, your expected value is (1/6)*200 + (5/6) * 50 = $75 --- less than the guaranteed $100.

Yes, by buying an index fund you accept the certainty that your returns will trail the index by a small amount. By picking stocks, you "gain" the possibility that you will outperform the index by a large amount --- but you also take on the risk that you will underperform the index much more severely than the index fund. This second outcome is much more likely, so the most likely outcome is that you will lose money relative to buying the index fund.

Perhaps most simply, your argument that the index fund guarantees "defeat" is incorrect. Underperforming the index is not defeat. Defeat is doing worse than some kind of average of other possible outcomes. We can quibble about exactly how to compute that average, but by any reasonable measure, index funds far outperform funds managed by professional investment experts, let alone average laypeople picking stocks. From 2011 through 2019, a majority of large-cap funds underperformed the S&P 500. Buying the index is victory; you beat 65% of professional fund managers. These funds were not just barely missing the index due to fees either; in 2019 the average large-cup fund trailed the index by eight percentage points. Unless your index fund is charging you 8% in fees, you are winning.

In a word, convenience. Same reason I, and I think most people, buy mutual funds in the first place. I don't have to spend time thinking about which particular stocks I want to buy or sell, I can just log in to the mutual fund company's web site and transfer money. Takes a minute or two, vs the hours I would spend researching & trading individual stocks.

The bottom line is that I can invest my time and mental energy more profitably doing something I'm actually good at, rather than trying to get an extra 0.1 percent or so extra return on investments.