Why does the text state that The Lord took us out with a strong hand even though it was Moses who physically took the Jews out of Egypt?

The story uses personification in order to show the magnitude of The Lord's power. To say that He only used one strong hand, compared to helping us with all of His might, tells us that we cannot come close to fathoming His sheer being and power. The text attributes human characteristics to G-d, also known as anthropomorphism, in order to signify G-d's power and the magnitude of his abilities. 

The text says that The Lord took us out of Egypt with a strong hand, instead of Moses, to remind us that everything in the world happens according to his will. The Lord took us out of Egypt using Moses, His leader, as a connection to the people.