The first flu shot in your childhood, or if you're like me who didn't have flu shot in childhood, the first flu you get is important to your immune system.
The immune response which is first established either through flu shot or flu we caught continues to characterize us throughout our life. Our immune mechanisms are conditioned and primed by the first stimulus we get (either flu shot or flu, whichever comes first). This is the reason why many times the flu shots don't work when influenza contains a novel strain. These flu shots are powerless to redirect our immune systems against the novel influenza strains. This is called original antigenic sin.
The point here is that the first shot is important. You don't want your immune system to be primed/conditioned with a leaky and flawed vaccine. It is not good for your future even this vaccine provides antibody which gives you temporary protection. Antibody protection is secondary protection and temporary protection. The most important immunity of your immune system is immunity from T cell and B cell which current vaccines are unable to do that.