Every time I hop on the treadmill at the LA Fitness, I am greeted by this quote, staring me down from across the room. When I first start running, I laugh it off as a cheesy gym saying. Near the end of hard runs, I tend to get a little philosophical in my misery, and I realize how true weakness can beat your morale down. Just because a run felt near impossible to complete today, does not mean that it will feel the same tomorrow. This is true for any endeavor.
For example, during the school year, I have days where everything seems to go wrong. Perhaps one of my lessons completely bombed or the students acted out of control. I'm tired. I'm stressed. I think to myself, "I suck as a teacher. This is a downward spiral. It's just the start. These students aren't going to learn anything with me..." (Yes, I tend to be a little over dramatic). But then, I stop, and I pinpoint exactly what went wrong and my plan to fix it tomorrow. Identifying my weakness on a bad day usually results in me becoming a better teacher.
I have this complete breakdown in running as well, usually during marathon training. Those times when I feel that I can't keep up with the rest of the group or when I stop to walk, it helps to tell myself that this is just one moment. Whatever may be a weakness now, will feel stronger the more that I push myself.
So cheesy saying on the gym wall, you are correct. Never let weakness convince you that you lack strength.