The cut-and-choose technique is used to prevent a malicious party who can construct garbled circuits incorrectly: because they are encrypted, the receiver can't realize if the sender is cheating. So the cut-and-choose technique works by demanding that the garbler constructs many copies of the required circuit, and open some of them to check.
In order to reach that verification, the garbler commits to his/her inputs, and both parties use oblivious-transfer protocol to realize the cut-and-choose.
So, because commitment and oblivious-transfer are used in this malicious resistant garbled circuit example, the security of this construction depends on the fact that protocols are or are not secure when you consider a computationally unbounded garbler. For example, if the commitment protocol used is not perfect binding... a unbounded grabler can cheat.