First impressions count a lot. There are many reasons for that:
1. You may not meet again.
2. The first mental picture is usually very strong & hard to replace.
3. We have been taught to do so.
But what about meeting people on their bad days? On days they were nervous & were trying desperately to fit in? What if they were supposed to be somewhere else but squeezed out a few seconds to meet you & others in the gathering? What if they were mourning or recovering from a tragic event? What if they were ill?
And this goes for people who fake it during the first meet. A second impression may help you see through their fakeness & shallow facade.
Don't lose a potential deal, co-founder, collaboration or endorsement because you hastily created a mental picture of someone before getting a chance to really meet them.
Allow people a chance to make a second (or third) impression.