Mechila that May Be Lacking

[Reuven rented a house to Shimon for a year. Reuven swore he would not remove Shimon form the house during that time, and Shimon swore he would not leave it unoccupied. The two got into an argument, in whose course Reuven told Shimon to vacate the house. Now Shimon wants to end the lease, and Reuven has retracted his statement, which he claims was not said seriously.]

First we must analyze Reuven’s statement (literally, "empty the house"). Vacating the house would seemingly indicate an exemption from paying rent, and an oral mechila (relinquishing rights) is binding. (See Sanhedrin 24a, regarding one who was obligated to swear to be exempt and his counterpart lowered the severity of the required oath). On the other hand, Reuven did not explicitly relinquish rights to rent. It is possible that he demanded that Shimon move out and yet continue to pay [even if this sounds like an unreasonable demand].
We find cases where one party makes a demand which seems to imply exemption and yet an explicit expression of exemption is needed. For example, when a lender tells his borrower to throw him the money he owes, the borrower is responsible for subsequent loss of the money unless the lender states he will be exempt as a result (Gittin 78a). In order to reconcile this with a mishna (Bava Metzia 98b), which says that when one returns money per instructions he is exempt, we must distinguish between repaying a loan and returning one’s object. A loan creates a monetary obligation that must be actually paid or relinquished. In contrast, when one is watching an object, as long as he follows the object’s owner’s instructions, there is nothing to obligate him. Another sugya where we see that mechila of payment must be explicit is Bava Kama 93a, where it says that it is not enough to tell someone, "Rip my garment," but he has to say, "Rip my garment on condition that you are exempt."
Furthermore, even if Reuven intended that if Shimon vacates he will be exempt from rent, that would only take effect if Shimon would have vacated before Reuven rescinded his statement. If this is not so, then Shimon would have been able to decide whether he wanted to continue the lease or break it, and it is unlikely that Reuven would allow Shimon to decide what he prefers.
Another factor is that when one does mechila that can be explained in different ways, we accept it as mechila only regarding lesser matters (see Ketubot 83a). In this case, the oath implied that Shimon originally was not permitted to vacate the house even if he were to continue to pay rent. Therefore, in the face of lack of proof, we will understand that the mechila was to allow him to move out but only if he is willing to pay.
Yet another factor is that binding decisions can be made without an act of kinyan, but at times there are reason to suspect that they do not represent the thought out decision of the one who uttered the statement and require confirmation (see Rambam, Mechira 5:13). The case of mechila made in anger is an example of something that is not binding without making sure that it represents his rational position.