Logistic regression essentially means taking the logit of your response proportions, p, and then doing standard regression. Consider the case where one p is 1. 

logit(1) = log(1/(1-1)) = infinity. How can you do regression with infinity?

That is, if one of your observed proportions p is 1, then you are trying to find the line that minimises the sum of squared differences from a set of points that include infinity. How does this not drive the regression line to always have infinite slope?