This verse would have us believe that God took the Jewish people out at night.  However, it is clear that the Jewish people left Egypt in the day, not the night. Why would the Torah change the narrative of when the Israelites left Egypt?

Rashi explains that while it is true that the Jewish people left Egypt in the morning, they were given permission to leave Egypt by Pharaoh the night before. The moment in time when they were given permission to go is therefore when God took them out of Egypt.

We think of freedom and jail as binary opposites. If one is free, one is by definition not incarcerated, and when one is incarcerated, one is not free. The idea that one can be incarcerated and at the same time free shows incredible depth of thought.  

The Jewish people did not leave Egypt until the next day, but that night, while they were still wearing the clothes of slaves and sleeping in the beds of slaves, they were free men and women. The knowledge they would be able to go and do as they wished was sufficient to make them free even as they still stood shackled in their chains.
Freedom is therefore not about being in a specific space, it is about a specific frame of mind.  People can be completely free, and yet they are slaves because their minds restrict them to what they believe they are capable of, or what their circumstances allow.
 
Others can be imprisoned in solitary confinement, and yet they are truly free, because they feel that freedom is not dependent on place, but on their state of mind.
We proclaim in the Haggadah, “Now we are slaves, next year we will be free men”.  Perhaps the Haggadah  is alluding to exactly this: we may be physically free, but perhaps we are still bound by our perceptions of the limitations we possess. We end with the optimistic thought that one day, we can break those perceptions and be truly free.