  The physics regarding the existence of the critical end point (CEP) on the
QCD phase boundary still remains unclear and its precise location is quite
uncertain. In this paper we propose that the hard-core size of the baryons used
in the description of the hot and dense hadron gas (HG) plays a decisive role
in the existence of CEP. Here we construct a deconfining phase transition using
Gibbs' equilibrium conditions after using a quasiparticle equation of state
(EOS) for QCD plasma and excluded-volume EOS for the HG. We find that the first
order transition results only when we assign a hard-core size to each baryon in
the description of HG and the phase boundary thus obtained terminates at CEP
beyond which a cross-over region occurs. The mean field approach for the HG
lends support to this finding where unless we include an excluded-volume effect
in the approach, CEP does not materialize on the QCD boundary. This
investigation provides an intuitive reasoning regarding the origin of CEP and
the cross-over transition on the QCD phase boundary.
