The human brain likes to think in narrative, and so we're drawn to those threads in life that exhibit clear dramatic arcs and momentous turning points. We retell those events that make good stories, and massage our own recollections to make a better story. This is not necessarily a bad thing -- I'm attracted to the somewhat existentialist idea that part of the way we figure out who we are and where we should go is reconstruct the story of what we've been up to so far, reassigning significance to events (and thereby actually changing their significance because our reconstruction changes those events' impacts on our future actions).
The idea of the "click" moment treats the philosophy in question more like a logical proof. With a logical proof, it makes sense that once you see its soundness, you have no choice but to suddenly agree with it then and there. But many philosophies that we might expect to "click" are more like ways of life. While they may surely be logically justified, they are broader and their implications are more intertwined into everything else -- they lack the clean simplicity of a logical proof. And ways of life don't just coerce us with the power of the better argument, a sort of cognitive offer we can't refuse. Ways of life are accepted through a process that also involves getting comfortable and familiar with them, and gaining practical skills of living in them (though this process may certainly be peppered with small or large epiphanies that can take on the character of "click" moments).
It's a potential pitfall to go around expecting or hoping other people will have "click" moments. It can easily lead to focusing too much on finding just the right argument, the mot juste that will cause the scales to suddenly fall from your adversaries' eyes, bringing them suddenly over to your side (either creating such a thing on the spot, or assembling an arsenal of certified "click"-inducers). It can enable a sort of "share your 'click' moment" rite of passage that elevates those with the best -- in the sense of making the best story -- "click" moments (or encourages them to elevate themselves) into spokespeople and subtly marginalizing those who don't have such good stories. And it may even encourage the canonization of certain arguments or experiences as certified "click"-inducers, such that people who have been exposed to them but haven't "click"ed over to the target philosophy can be dismissed as willfully ignorant or a lost cause.
On the other hand, too much concern for the slowness of philosophical change can lead to softpedaling people's accountability for pushing themselves to change. Just because it may psychologically take time to accept and adjust to a new way of thinking doesn't mean that the person isn't still in the wrong while they're transitioning.