Magnetization reversal of exchange biased synthetic antiferromagnet (SAF) was analyzed at the initial stage back to the exchange biasing direction, based on the single domain assumption of each layer. Both static and dynamical methods were employed wherever appropriate. Results show that the reversal process can either start from an asymmetric continuous rotation of magnetizations or an abrupt switching of direction by any one or both magnetizations, and either layer can have the reversal priority over the other depending on materials parameters. In the limit of large interlayer coupling or large exchange bias, simple criteria were obtained for triggering a switching event in the system at the critical field of instability, as well as reversal priority flipping of the two layers. Interlayer antiferromagnetic coupling tends to prevent magnetic switching, and helps the reversal of the pinned layer. The results reveal the interplay of interlayer coupling, exchange bias, and magnetic anisotropy in governing the complicated magnetization behaviors of exchange biased SAF.