Catholics can accept evolution because the pope does.
'Pope John Paul II revisited the question of evolution in a 1996 a message to the Pontifical Academy of Sciences. Unlike Pius XII, John Paul is broadly read, and embraces science and reason. He won the respect of many scientists in 1993, when in April 1993 he formally acquitted Galileo, 360 years after his indictment, of heretical support for Copernicus’s heliocentrism. The pontiff began his statement with the hope that “we will all be able to profit from the fruitfulness of a trustful dialogue between the Church and science.” Evolution, he said, is “an essential subject which deeply interests the Church.” He recognized that science and Scripture sometimes have “apparent contradictions,” but said that when this is the case, a “solution” must be found because “truth cannot contradict truth.” The Pope pointed to the Church’s coming to terms with Galileo’s discoveries concerning the nature of the solar system as an example of how science might inspire the Church to seek a new and “correct interpretation of the inspired word.”
When the pope came to the subject of the scientific merits of evolution, it soon became clear how much things had changed in the nearly since the Vatican last addressed the issue. John Paul said:
Today, almost half a century after publication of the encyclical, new knowledge has led to the recognition of the theory of evolution as more than a hypothesis. It is indeed remarkable that this theory has been progressively accepted by researchers, following a series of discoveries in various fields of knowledge. The convergence, neither sought nor fabricated, of the results of work that was conducted independently is in itself a significant argument in favor of the theory.
Evolution, a doctrine that Pius XII only acknowledged as an unfortunate possibility, John Paul accepts forty-six years later “as an effectively proven fact.” (ROA, 82)'
http://law2.umkc.edu/faculty/projects/ftrials/conlaw/vaticanview.html