If a story, an excuse, or an idea is implausible, it is difficult to believe, and so it is unlikely to be true. It does not fit what we know about how the world works. It is softer than impossible: impossible cannot happen; implausible could happen, but you would not bet on it. Scientists, lawyers, and reviewers use it a lot. Though actually, people also stretch it for “a bit too convenient” — an implausible coincidence in a film. Neutral to formal; you can say it in class. It is not the same as “I do not like it.” You are talking about belief, not taste.