If you are the kind of person that just wants to go along without having to think about your gear while on a leisurely dive, and you know that you are not the type to pay attention, then a rebreather is not for you. If you are the type that is diligent and pays attention to what is going on during the dive, then a rebreather can actually be safer than open circuit diving.
A rebreather buys a tremendous amount of time for the diver when things do go wrong. For instance, if you are way back in a cave and you experience a complete silt out and become separated from the line (which is a no-no in itself), you can park, wait an hour for the silt to clear, search for the line, and take your time getting out without missing any decompression obligation. If you get lost inside a wreck or entangle, you can take as long as you need to get yourself out of the situation. You have more than enough breathing gas to last for hours no matter what the depth. This is huge!
Even if a component fails, there are still many options for the rebreather diver that are not available for the open circuit diver. For example, if your unit starts having the CCR equivalent of a free flow, shooting gas into the unit, you can shut that portion of the unit down and fly the unit using an alternative that gives you just as much time as if your unit were working 100 percent. If a problem occurs, there can be several alternatives to the rebreather diver rather than just "it works or it doesn't." You learn about all of these methods in your training.
For some diving, a rebreather makes life much easier. If you want to see a dive that is a perfect example, just download
this link. (Just so you know, it is HD video, and it will take a long time to download, maybe 45 minutes depending on connection speed. However, I assure you that you will enjoy the footage.) If we had done this dive on open circuit, we would have had to make two dives instead of one, dropping lots of open circuit tanks along the way to make sure we would have enough gas to get to our destination and back. The actual dive was about three hours 15 minutes, and the average depth was about 120 feet.