They think they do, however, due to two problems. One is pride, the other is a very small imagination.
On the pride front, secularists believe that if they have decided something is true then everyone will eventually agree with them. If someone disagrees it is due to the fact that the someone either doesn't have access to the same facts or isn't bright enough to figure out what the secularist is saying. The idea that someone may be bright, have access to the same facts, and draw a different conclusion is a foreign idea. I can still remember the dismay of my friends in college when they would tell me some fact that they thought would blow the whole argument out in the open and I would say, "I know that. SO????"
They also have very little imagination. They think that the way things are now is the only reasonable way they would or could be. In America we have a basically moral society because we are still drawing on the "moral bank account" left to us by previous generations. Many of us realize this and recognize that the account is depleted if not overdrawn. But the secularists think that America is so moral because morality is obvious and any casual observer would establish property rights, personal rights, etc, the same way that we have them established now. The idea that a rational argument (absent a moral authority) could be made for a society where murder is not only legal but encouraged is beyond their imagination. However, they don't recognize the limits of their imagination due to pride (see previous paragraph).
In the end, they trip themselves up because they insist on rights based on some limited notion of reality that they can not defend, but must demand you accept as axiomatic.
Shalom.