"I know people think I'm nuts," the embattled Rodriguez told USA Today Sports. "I know most people wouldn't want the confrontation. Most people would say, 'Get me out of here. Trade me. Do anything.'
"But I'm the [expletive] crazy man who goes, 'I want to compete. I want to stay in New York. I refuse to quit.'
"Maybe it's stupidity, I don't know, but I'm wired to compete and give my best. I have a responsibility to be ready to play as soon as I can."
Making his way back from hip surgery that has sidelined him the entire season, Rodriguez has been a lightning rod for criticism throughout his tenure with the Yankees.
A three-time MVP, Rodriguez once again is embroiled in controversy, denying allegations that he received performance-enhancing substances from a Biogenesis clinic in South Florida. A-Rod also received sharp criticism recently from Yankees general manager Brian Cashman on a tweet about his rehab process.
Rodriguez told the paper that despite all the critics, he still has the drive to persevere.
"You hear all of the doubters," he said, "and that just fuels me. They don't know me. I'm not giving up. I never will. I'm not wired that way.
"This is the hardest fight I've ever had. There have been days, like, 'Holy [expletive], how am I going to get through this day?' But you keep getting after it, keep pushing."
The 37-year-old Rodriguez, who has 647 career home runs, went on to say that he's never considered walking away from the game.
"The easy thing would be to give up," he said. "But I didn't get to where I am by taking the [expletive] way out. I refuse to start now.
"There's a lot of fight left in me."
It's uncertain exactly when Rodriguez will return to the Yankees. He's played in two minor league rehab games and said he'll need about 20 before being ready to return to the majors.