To explore the origin of glassy transition and glass-forming abilities (GFAs) of transition metal-transition metal (TM-TM) alloys from the microstructural point of view, a series of molecular dynamics (MD) simulation for the rapid solidification processes of liquid Cu56Zr44alloys at various cooling rates and pressures P are performed by using a LAMPS program. On the basis of Honeycutt-Andersen (H-A) bond-type index (ijkl), we propose an extended cluster-type index (Z, n/(ijkl)) method to characterize and analyze the microstructures of the alloy melts as well as their evolution in the rapid solidification. It is found that the majority of local atomic configurations in the rapidly solidified alloy are (12 12/1551) icosahedra, as well as (12 8/1551 2/1541 2/1431) and (12 2/1441 8/1551 2/1661) defective icosahedra, but no relationship can be seen between their number N(300 m K) and the glassy transition temperature Tg of rapidly solidified Cu56Zr44alloys. By an inverse tracking of atom trajectories from low temperatures to high temperatures the configuration heredity of icosahedral clusters in liquid is discovered to be an intrinsic feature of rapidly solidified alloys; the onset of heredity merely emerges in the super-cooled liquid rather than the initial alloy melt. Among these the (12 12/1551) standard icosahedra inherited from the super-cooled liquids at Tm-Tg is demonstrated to play a key role in the formation of Cu56Zr44 glassy alloys. Not only is their number N300 KTgP inherited from Tg to 300 K closely related to the GFA of rapidly solidified Cu56Zr44alloys, but a good correspondence of the onset temperatures of heredity (Tonset) with the reduced glass transition temperature (Trg= Tg/Tm) can be also observed. As for the influence of and P on the glassy transition, a continuous tracking of descendible icosahedra reveals that the high GFA of rapidly solidified Cu56Zr44 alloys caused by big and P can be attributed to their elevated inheritable fraction (fp and ftotal) above Tg.