Warning--no analogy is perfect. Especially one originating in my mind. But there is something about the following that helps me explain why I believe in prophets even though they can be "wrong".
Parents aren't perfect. At least mine weren't. Yet I love my parents immensely. As a kid all I wanted to do was make my parents proud of me. They were great people in my eyes. (They still are--I just think the analogy works better if I'm using a parent/child relationship). I trusted them. I knew they wanted what was best for me. I knew that they knew things I didn't know. They had experienced things I hadn't, and could "see" things I couldn't from my vantage point. I even believe they received revelation and inspiration on behalf of our family. They taught me things of great value. They taught me truth--things that have made my life better and happier has a result.
Sometimes they were wrong. However, the things they got right far exceeded the wrong, so I never had to question whether or not following their teachings was ultimately leading me in the wrong direction or in the right direction.
No mortal alive today is perfect. In fact, only one who ever walked the earth was perfect--Jesus Christ. We trust in Him and in the Spirit who guides us into "all truth" (John 16:13). We can't look to mortals (prophets included) and expect to always get perfection. We can only look to Perfection to receive perfection. But by golly, I'm grateful God gave me my parents. And I'm grateful he gives us modern prophets too.