I know everyone says that the best time to take a HPT is first thing in the mornings, but why is that? Aren't they accurate at all times if you have missed your period?

A urine pregnancy test is testing for the pregnancy hormone hcg. While if you are pregnant, it is always present in your urine it's concentration becomes diluted. You drink fluids during the day, and elminate mulitple times. If you use your first morning urine, you have slept all night without drinking or going to the bathroom, allowing hcg to build up and be more concentrated.

So early during a pregnancy... say you tested in the late afternoon/evening. Your concentration of hcg is not going to be as high as it would be right when you wake up... thus possibly causing a false negative test.