The "vice versa" part of this statement is utter bullsh!t -- which is why "causality is difficult to prove." In fact, the historical record shows the exact opposite: For most of this country's history abortion was a crime in most states while the execution of criminals was considered an accepted form of punishment. Capital punishment began to lose its appeal at almost the exact same time in our history (the 1960s) that many states began to legalize abortion.
In our modern secular culture, there is no longer any rational reason for the U.S. not to execute criminals -- even if an innocent person is occasionally executed in the process. A nation that executes more than 4,000 unborn children every day should have no qualms about killing grown-ups with boring regularity.
"In our modern secular culture, there is no longer any rational reason for the U.S. not to execute criminals--even if an innocent person is occasionally executed in the process."
And miscarriages of justice are rare, certainly more rare than in the past, where the law didn't seem all that interested in waiting 10-20 years to ascertain guilt and put murderers to death.