@Drew that is a great question! Interest rates act as gravity for stock prices. This happens for many reasons, but if you have individual companies relying on cheap credit to increase their profits, they will be highly affected by interest rates.
Also, companies having to reinvest large amounts of money into their assets (like machinery for example) will find that in high interest rate environments there may also be higher inflation, and they may have to borrow money to reinvest into those assets. This will hold profits down for these companies for these reasons.
These are just a couple reasons out of many, why interest rates have an important impact on individual companies. As this continues to happen while interest rates rise, you will find a higher dispersion between individual companies returns inside an index.
Taking the reasons above, if you have companies not needing to invest large amounts into their assets, or needing to borrow money to increase profits, there will likely be a higher dispersion inside the index between that groups returns and the group relying on low interest rates.
The mutual funds have the ability to cherry pick these companies, while the index does not. These are just a couple reasons why stock pickers could benefit from higher interest rates. Whether or not the mutual fund managers would be smart enough to pick the companies as a whole is in question, but it should definitely make it harder for some companies to increase profits, which will benefit the stock price of companies not impacted by interest rates.
It is hard to pick individual stocks as a "rising tide lifts all boats".