Definitions for "Reciprocate"
To move forward and backward alternately; to recur in vicissitude; to act interchangeably; to alternate.
To give and return mutually; to make return for; to give in return; to interchange; to alternate; as, to reciprocate favors.
Alternate backward and forward motions - Oxford Dictionary.
This is a more sophisticated way of saying "do me like I do you," but it works for non-sexual contexts as opposed to "giving and receiving." It can refer to something as nebulous as "have exactly the same degree of passion I have." In this case, better investigate further.