In 2012, McDonald's (MCD  ) made a pledge to work with its suppliers to phase out the use of gestational crates, tiny boxes used to house pregnant sows. The crates have been repeatedly singled out by animal rights advocates as being inhumane. Now, billionaire investor and McDonald's shareholder Carl Icahn is accusing the company of failing to live up to that pledge.

Icahn owns 200 shares in the fast-food chain, and he's pushing for two candidates of his choice to be added to the executive board. Experts expect Icahn's campaign for better treatment for the pigs sourced for McDonald's products to be met with considerable pushback from the company.

Part of the reasoning in support of that potential pushback is McDonald's financial strength. Corporate agitators tend to go after companies that are failing or weak. McDonald's, on the other hand, has seen a stock increase of 18% over the past year.

Another point in McDonald's favor is the relatively small size of Icahn's stake in the company. However, recent projects by activist investors with small stakes have seen success. Last year, activists were able to add two members to ExxonMobil's board in an effort to influence the company's climate strategy.

According to McDonald's, Icahn is nominating Maisie Ganzler and Leslie Samuelrich to be added to the company's board of executives. Samuelrich is the president of an investment fund with a focus on sustainable energy, Green Century Capital Management. Ganzler serves as chief of strategy and brand officer at Bon Appétit Management Company.

The gestation crates at the heart of Icahn's cause are used to ensure that all sows are able to receive the right amount of feed. Producers and pig experts say that, in a communal space, more dominant sows hoard all of the feed, stopping weaker sows from getting the nutrition they need. Other methods of addressing the issue have reportedly also had issues.

Most gestation crates are around 2 feet by 7 feet, meaning they're too small for the sows to be able to turn around. The confinement and limited movement can cause a number of health issues, from urinary tract infections and overgrown hooves to weakened bones and mental stress.

Icahn told reporters that McDonald's pork suppliers are still using the crates for a significant portion of the sows' pregnancy.

In response to Icahn's allegations, McDonald's released a statement claiming that the chain has actually been ahead of other restaurants when it comes to committing not to use gestation crates. The company also stated that the issue "has already [been] introduced through a shareholder proposal" from the U.S. Humane Society.

"The Company sources only approximately 1% of U.S. pork production and does not own any sows, or produce or package pork in the United States," the company writes. "Nevertheless, in 2012 it became the first major brand to make a commitment to source from producers who do not use gestational crates for pregnant sows."

The fast-food chain wrote that it expects at least 85% of its pork to be sourced from sows not housed in gestation crates by the end of this year. The 100% goal is set for 2024.

The company also argued that Icahn's demands would be "impossible" to meet given the current state of pork production. It also pointed out Icahn's majority ownership in Viskase, a pork and poultry producer and packer.

"Mr. Icahn's ownership provides him with unique exposure to the industry-wide challenges and opportunities in migrating away from gestation crates," the statement reads. "Thus, it's noteworthy that Mr. Icahn has not publicly called on Viskase to adopt commitments similar to those of McDonald's 2012 commitment."

Icahn's board nominations will be evaluated like any other candidates, according to McDonald's.