The best way to convince a client they are making a mistake is to do it the way they asked and do it the way you think is better and then show them both. Sometimes the client sees their error. Other times it turns out that the client has an unarticulated need that gets teased out and the final design incorporates both the ideas of the designer and the unarticulated need.

It's important to realize, that often the client is more experienced with their requirements, i.e. the business domain. And their understanding may be sophisticated in ways that are contrary to the naive take of an outsider.