  The independent measurement of Hubble constant with gravitational-wave
standard sirens will potentially shed light on the tension between the local
distance ladders and Planck experiments. Therefore, thorough understanding of
the sources of systematic uncertainty for the standard siren method is crucial.
In this paper, we focus on two scenarios that will potentially dominate the
systematic uncertainty of standard sirens. First, simulations of
electromagnetic counterparts of binary neutron star mergers suggest aspherical
emissions, so the binaries available for the standard siren method can be
selected by their viewing angles. This selection effect can lead to $\gtrsim
2\%$ bias in Hubble constant measurement even with mild selection. Second, if
the binary viewing angles are constrained by the electromagnetic counterpart
observations but the bias of the constraints is not controlled under $\sim
10^{\circ}$, the resulting systematic uncertainty in Hubble constant will be
$>3\%$. In addition, we find that both of the systematics cannot be properly
removed by the viewing angle measurement from gravitational-wave observations.
Comparing to the known dominant systematic uncertainty for standard sirens, the
$\leq 2\%$ gravitational-wave calibration uncertainty, the effects from viewing
angle appear to be more significant. Therefore, the systematic uncertainty from
viewing angle might be a major challenge before the standard sirens can resolve
the tension in Hubble constant, which is currently $\sim$9%.
