Never mind that just a few weeks earlier, the billionaire investor Nelson Peltz had launched a very public proxy battle against her company. Peltz, the 72-year-old co-founder of the $11 billion hedge fund Trian Fund Management, is one of the most high-profile and accomplished of Wall Street’s growing hoard of so-called activist shareholders. And he wasn’t pulling any punches. Kullman, 59, was frustrated that Peltz was trying to paint her giant chemical company, the inventor of wonder fabrics such as nylon and Kevlar as well as one of the biggest players in the business of providing hybrid seeds to farmers,...