Abstract We study the physical mechanisms that cause the offset between low-redshift and high-redshift galaxies on the [O iii]λ5007/Hβ versus [N ii]λ6584/Hα “Baldwin, Phillips & Terlevich” (BPT) diagram using a sample of local analogues of high-redshift galaxies. These high-redshift analogue galaxies are selected from the Sloan Digital Sky Survey. Located in the same region on the BPT diagram as the ultra-violet selected galaxies at z ∼ 2, these high-redshift analogue galaxies provide an ideal local benchmark to study the offset between the local and high-redshift galaxies on the BPT diagram. We compare the nitrogen-to-oxygen ratio (N/O), the shape of the ionising radiation field, and ionisation parameters between the high-redshift analogues and a sample of local reference galaxies. The higher ionisation parameter in the high-redshift analogues is the dominant physical mechanism driving the BPT offset from low- to high-redshift, particularly at high [N ii]λ6584/Hα. Furthermore, the N/O ratio enhancement also plays a minor role to cause the BPT offset. However, the shape of the ionising radiation field is unlikely to cause the BPT offset because the high-redshift analogues have a similar hard ionising radiation field as local reference galaxies. This hard radiation field cannot be produced by the current standard stellar synthesis models. The stellar rotation and binarity may help solve the discrepancy.