[Singukil]

While I agree that the term Hinayana should be
dropped....

Absolutely, LazyEye. It is an unnecessary and pejorative term which is still used both offline and online.

..... I notice that the booklet's authors indulge in some fairly blatant sectarian propaganda of their own-- in particular, they trot out the highly disputable claim that the Mahasanghikas (precursors of the Mahayana) were the first group to split from the unified sangha, and that the Sthaviras (proto-Theravadins) represented "the original sangha from which the other schools seceded".

From a different source - the respected Access to Insight website where we are able to read Pali Canon suttas online :

100 years after the Buddha's Parinibbana the Second Council convenes in Vesali to discuss controversial points of Vinaya. The first schism of the Sangha occurs, in which the Mahasanghika school parts ways with the traditionalist Sthaviravadins.

At issue is the Mahasanghika's reluctance to accept the Suttas and the Vinaya as the final authority on the Buddha's teachings. This schism marks the first beginnings of what would later evolve into Mahayana Buddhism, which would come to dominate Buddhism in northern Asia (China, Tibet, Japan, Korea).

http://www.accesstoinsight.org/history.html