Short explanation: The simple truth is that the Church still highly recommends this devotional prayer. The rosary is praised in the  CCC  (sections 971, 1674, 2678, and 2708) and has been highly praised by all recent popes. If anything, the Rosary is exactly what we need these days.

More complete explanation:

This is an error commonly presented in books, seminars, and even university lectures (proximate to heresy at best; covertly, diabolically, and perniciously anti-Catholic at worst), and believed by gullible people who have a pathological need to feel like they are on the cutting edge of theological and liturgical evolution. Unfortunately, this means that most of the people who believe this lie are well-read and well-educated. Having spent so much of their time and money reading and learning this stuff, they are now loathe to admit that the books, seminars, and universities they chose were actually worthless, or even worse, toxic to the faith. They would have been spared this indignity if they had read actual Church documents instead of blindly swallowing unreliable books, seminars, and university lectures.

Related Catholic Trivia: There used to be a friendly debate about whether or not it was proper to wear the rosary around one's neck. Nowadays it might be better not to do so, since wearing one has become a kind of social commentary by punk rockers and their ilk. The rosary is a blessed sacramental, intended to be used as a counting device during prayer. Therefore, it is inapproppriate to treat it like some lowly piece of bling-bling. Besides which, Jesus railed against ostentatious religion, and wearing a rosary is about as religiously ostentatious as one can get. However, the Church does not forbid wearing the rosary, and it might be acceptable in some cultures, so don’t get all bent out of shape if you see it.