It's very easy to confuse 'being ill' with 'being infectious'. Those are only loosely related. You're generally infectious when the amount of virus particles in your airways is the highest. But influenza symptoms can exist long after you have cleared the virus from your system. The damage the viruses did can linger for days to weeks to years. The post-viral syndrome (now often referred to in the context of COVID-19 as post-COVID) is a real issue for a lot of people.