I agree that some people are better off staying single. If you are content to remain single and choose that, that is great. I would wholeheartedly agree that not everyone should get married. You shouldn't feel under pressure to enter marriage. I think the saying that is being discussed in this OP is referring to those who genuinely desire to be in a relationship. I don't think it is a statement about marriage being for everyone. I see it is an encouragement to those who desire to meet others.
Obviously, this isn't a Biblical quote. As Christians, we can't marry someone who isn't a believer. So, we may have more difficulty than non Christians do in meeting someone. We have to look for spiritual compatibility in addition to all the other aspects most loom for in a spouse. It definitely narrows down our field, but I still think the saying has some truth to it.