I've gotten this question at the beginning of every class I've ever taught. I've even had students who have said "since I always narrow it down to two and then pick the wrong one, I've started choosing the one I didn't want to pick in the first place--and now I still pick the wrong one." Ouch. What's going on here? Well, you might not like my answer, but I'm not going to bullshit you. On the LSAT, if you think you always narrow it down to two answers and pick the wrong one, you're simply fooling yourself. You're operating under an illusion. The sooner you understand this illusion, the sooner you'll get down to the business of understanding your mistakes and picking more correct answers.
The truth is that you don't actually pick the wrong one every time. If you narrow it down to two answers, you're going to end up being right about half the time and wrong about half the time. But since you only mark the incorrect questions wrong, you only end up reviewing the questions where you've guessed wrong. This is called selection bias. And then, after a matter of time, you develop a psychosis about "always picking the wrong one." The questions where you narrowed it down to two and picked the wrong one start to jump off the page at you. You really notice every time you do it--it burns into your retinas. This is called confirmation bias.
You might not believe me, but I'm pretty sure I can prove it to you. Next time you take a test, simply circle every question where you narrow it down to two answers. When you correct the test, you'll see that you got a number of these questions right. But you never would have looked at them again if you didn't circle them in the first place. Sorry to get all scientific and boring and common-sensical on you. Superstition, religion, and other metaphysical nonsense play no role on the LSAT. The LSAT is about logic, plain and simple.
The happy truth here is that if you can narrow it down to a 50-50 guess, you're starting to get it! Half the battle on the LSAT is avoiding the truly terrible answers. If you can do that, congratulations. Your next step will be figuring out what's conclusively better about the correct answer, or what's conclusively inferior about the second-best (incorrect) answer. Stop worrying about "always picking the wrong one" and focus on what's wrong with the answer you picked. With time, you'll get there. I promise that it's easier than you think.