Former New York Stock Exchange President Tom Farley told CNBC on Monday he isn’t so sure his old rival, the Nasdaq, should be considered a benchmark for technology stocks.

When he hears and sees the term “tech-heavy Nasdaq Composite index,” Farley said it drives him “nuts.”

“This isn’t even a tech index,” he argued on “Squawk Box” from the Nasdaq MarketSite in Times Square. “I mean, Bed Bath & Beyond? Why are they acting like this is a tech index? It was free branding for my competitor.”

Bed Bath & Beyond and many other non-tech stocks trade on the Nasdaq, which did not immediately respond to CNBC’s request for comment.

Farley did admit, “It felt a little weird walking into this building this morning,” referring to the Nasdaq MarketSite, where the “Squawk Box” studio is located. Farley is now chairman and CEO of Far Point Acquisition, a blank-check company he helped form with Dan Loeb’s hedge fund Third Point.

The NYSE — one of the largest equities-based exchanges in the world — trades billions of shares each day for thousands of companies, including some tech stocks including Twitter and Alibaba.

But the Nasdaq is home to the biggest American tech giants: Apple, Amazon, Microsoft, and Google’s Alphabet.

Farley, who ran the NYSE from November 2013 to May 2018, characterized the rivalry between the two exchanges to that of the Hatfields and McCoys, the two mountain clans on the West Virginia–Kentucky border who waged a bitter feud in the late 1800s.

“The Hatfields and McCoys competition really, truly did benefit the listing companies,” the companies holding initial public offerings or IPOs, said Farley, who added he has “tremendous” respect for the Nasdaq and the people who run it.

However, he said, “I woke up everyday trying to kill them.”

Still, the NYSE has opened up more to other exchanges. Earlier this year, The NYSE ended a decades-old restriction that prevented stocks listed on rival exchanges, including the Nasdaq, from being bought and sold on its trading floor.