Why is the current temperature sometimes lower than today's low temperature? For example right now it 13F with a predicated low today of 16F!

a) Forecasts are very resource-intensive, they are performed on a specific schedule using a computational forecast model. Updating the predictions would require inputting new data and running the model again, and by the time they do that, the next forecast will already be out.

b) Do they know it's wrong? Where did you get the temperature? From an official weather station? If not, there is no reason to imagine that someone is noticing that this one particular model run was wrong in one particular spot across the whole country and trying to fix it in real time.

c) If you did get the current temperature from an official weather station, that IS your update for it. Real time data from official weather stations is always going to trump the forecast model. What would be the point of updating the forecast when the current measured data from the weather station is now available? That's like driving down the highway and saying "I was predicting my speed would be close to 65mph, but due to the heavy traffic I'm seeing today, I'm going to re-estimate my speed to be 45mph" when you have a perfectly accurate speedometer right in front of you telling you exactly what speed you are going at all times. Forecasts are only useful for the future, and they can be wrong.