Does Dawkins need God to be good?

While I have to admit that I am not a fan of Richard Dawkins' rhetoric, I found myself immediately agreeing with what he meant by the title of one of his most recent articles: “You don’t need God to be good ... or generous.” Leaving aside the 95% of the article where he attacks religion in his trademark ad hominem, populist manner (“as a matter of fact it probably is not the case”[emphasis mine]), it turns out that his argument simply is that non-believers too are capable of “selfless generosity.” Both this and his claim, which I would translate as “you don't need to believe in God to be good,” are statements that I wholeheartedly agree with and which are in line with the teachings of the Catholic Church. Here the Catechism (§33) affirms that we are all

“open to truth and beauty, [have a] sense of moral goodness, [have] freedom and the voice[s] of [our] conscience[s], with [our] longings for the infinite and for happiness.”

None of this is predicated on a belief in God. What I believe though is that it does come from God, who is the source of all goodness, generosity and love. This is where Prof. Dawkins and I would disagree.