You can blame (then NYC mayor) John Lindsey for that. When he made the deal for the refurbishment of (the original) Yankee Stadium, it included the stadium no longer allowing the Giants to play football there.
that's not accurate:
"Desiring their own home stadium, in the early 1970s the Giants reached an agreement with the
New Jersey Sports and Exposition Authority to play their home games at a brand-new, state-of-the-art, dedicated football stadium.
[70] Some New Yorkers were furious and Mayor
John Lindsay had attempted to keep the team in the city by proposing to buy Yankee Stadium and renovate it at a cost of $24 million. Lindsay estimated that they brought $3 million to the city, and was anxious to keep that revenue, as well as satisfy New York Giant fans.
[68] Axthlem characterized the Giants fan base at the time as mostly "white, suburban and fairly well to do, and its members drive cars to football games."
[69] The battle became nasty with members of the New York City side claiming that the Maras "complained of how inconvenient it was for
them to park, or for
them to get out to the neighborhood."
[69] They claimed the Maras "never really negotiated. They just listened...I think they were afraid if they asked for something, we might give it to them—and they wanted to keep us from offering a deal that they couldn't turn down."
[68] In fact, the Maras had already made the agreement to move out of the city, even though Wellington was still placating the city.
[68] He felt this was a factor in the Mara's decision to move the stadium, as the attendees could drive to their New Jersey stadium as opposed to traveling through the Bronx to Yankee Stadium.
[69] The new stadium, which would become known as
Giants Stadium, was to be built at a brand new sports complex in
East Rutherford, New Jersey.
[70] The decision met with outrage from some New Yorkers, and the city's mayor
John Lindsay sought legal action to prevent the team from playing in Yankee Stadium — or anywhere else in New York — and demanded a congressional investigation into the deal.
[65] "