When I find myself trying to persuade others of the advantage of approval and score voting, I often end up arguing with proponents of instant runoff voting. And after debunking the claim that IRV is immune to spoilers, their typical follow-up response is to bring up "bullet voting".
"Bullet voting" means that, even if a voter has the option in a voting system to rank or rate multiple candidates, they choose to only rank one. And so, their ballot is effectively equivalent to a plurality voting ballot. Since plurality is bad (a fact we can all agree on), any system that incentivizes it will also be bad.
My opponents argue that, if enough voters choose to approve of (or to give maximum points to) a second candidate—one other than their honest-favorite—that these voters could cause a worse result for themselves than if they had not done so. In other words, they could cause their true favorite to lose by approving multiple options; therefore, voters have an incentive to approve only one candidate, hence bullet voting, hence plurality-level results.
The truth is, they've actually pointed out the greatest strength that cardinal voting systems (like approval and score) have over ranked voting systems (like IRV and Condorcet systems): you might accidentally cause your second choice to win. But how is this an advantage? Because in those other systems, the risk is that you might accidentally cause your last choice to win! That's what the existence of spoilers in these systems mean, that when voters choose to support their true favorite above all others, they risk throwing the election to the candidate the hate the most; that, or they can play it safe, by supporting an acceptable, but not fantastic, candidate, at the expense of removing all hope for their true-favorite to win.
Meanwhile, while you sit in the booth contemplating your approval ballot, trying to decide whether or not to "bullet vote", your fear isn't of your least-favorite candidate winning, but of your second-favorite candidate winning. Now, that's still not going to be an easy choice, but your prospects seem much better when your choice is between 1st and 2nd rather than between 1st and last.