The assumption I started my last comment with is extremely important. I'm assuming we are referring to "the flu" as the disease not the influenza virus itself.
Disease is just a named collection of symptoms, that it. A vaccine absolutely can cause those symptoms, and when they occur together it would meet the definition of the disease. That obviously doesn't mean the vaccine caused an influence infection.
Few disease definitions actually take into account severity of symptoms. There are some examples where we have two named diseases where one is distinguished only by being more severe, but unless I'm missing something the flu doesn't fit into that category.
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The assumption I started my last comment with is extremely important. I'm assuming we are referring to "the flu" as the disease not the influenza virus itself.
Disease is just a named collection of symptoms, that it. A vaccine absolutely can cause those symptoms, and when they occur together it would meet the definition of the disease. That obviously doesn't mean the vaccine caused an influence infection.
Few disease definitions actually take into account severity of symptoms. There are some examples where we have two named diseases where one is distinguished only by being more severe, but unless I'm missing something the flu doesn't fit into that category.