Short explanation: A person whose conscience is 100% perfect would be able to say that the statement above is true. But for the rest of us imperfect folk, it’s false, because one’s conscience can be (and often is) wrong.
More complete explanation:
Conscience is not the voice of God in your head. It’s a faculty of your own mind: the faculty of judging what ought to be done. This faculty is not infallible. It’s only as good as we make it over a lifetime of careful moral formation.
Ever hear of the “garbage in, garbage out” principle of computer usage? It’s the same way with conscience. If your conscience was formed correctly, then it will judge right from wrong correctly. But if it was formed badly, it will judge badly. For example, suppose a boy is raised by pickpockets, and trained how to pick pockets from his childhood. His conscience will be malformed; it will not object to stealing at all. But stealing is in fact wrong. Therefore his conscience does not tell him what’s right or wrong. In fact, it tells him the opposite.
We therefore have a moral obligation to form our consciences correctly. This is done in many ways, most notably by paying attention to the infallible moral teachings of the Church. Since they are infallible, they are rock-solid foundations for a well-formed conscience.