  In this work, we revisit the isospin violating decays of $X(3872)$ in a
coupled-channel effective field theory. In the molecular scheme, the $X(3872)$
is interpreted as the bound state of $\bar{D}^{*0}D^0/\bar{D}^0D^{*0}$ and
$D^{*-}D^+/D^-D^{*+}$ channels. In a cutoff-independent formalism, we relate
the coupling constants of $X(3872)$ with the two channels to the molecular wave
function. The isospin violating decays of $X(3872)$ are obtained by two
equivalent approaches, which amend some deficiencies about this issue in
literature. In the quantum field theory approach, the isospin violating decays
arise from the coupling constants of $X(3872)$ to two di-meson channels. In the
quantum mechanics approach, the isospin violating is attributed to wave
functions at the origin. We illustrate that how to cure the insufficient
results in literature. Within the comprehensive analysis, we bridge the isospin
violating decays of $X(3872)$ to its inner structure. Our results show that the
proportion of the neutral channel in $X(3872)$ is over $80\%$. As a by-product,
we calculate the strong decay width of $X(3872)\to \bar{D}^0 D^0\pi^0$ and
radiative one $X(3872)\to \bar{D}^0 D^0\gamma$. The strong decay width and
radiative decay width are about 30 keV and 10 keV, respectively, for the
binding energy from $-300$ keV to $-50$ keV.
