  Many $z=1.5$ galaxies with a stellar mass ($M_{\star}$) $\geq
10^{10}\,\mathrm{M}_\odot$ are already quenched in both galaxy clusters ($>50$
per cent) and the field ($>20$ per cent), with clusters having a higher
quenched fraction at all stellar masses compared to the field. A puzzling issue
is that these massive quenched galaxies have stellar populations of similar age
in both clusters and the field. This suggests that, despite the higher quenched
fraction in clusters, the dominant quenching mechanism for massive galaxies is
similar in both environments. In this work, we use data from the cosmological
hydrodynamic simulations Hydrangea and EAGLE to test whether the excess
quenched fraction of massive galaxies in $z = 1.5$ clusters results from
fundamental differences in their halo properties compared to the field. We find
that (i) at $10^{10} \leq$ $M_{\star}/\,\mathrm{M}_\odot\leq 10^{11}$, quenched
fractions in the redshift range $1.5 < z < 3.5$ are consistently higher for
galaxies with higher peak maximum circular velocity of the dark matter halo
($v_{\mathrm{max, peak}}$), and (ii) the distribution of $v_{\mathrm{max,
peak}}$ is strongly biased towards higher values for cluster satellites
compared to the field centrals. Due to this difference in the halo properties
of cluster and field galaxies, secular processes alone may account for (most
of) the environmental excess of massive quenched galaxies in high-redshift
(proto) clusters. Taken at face value, our results challenge a fundamental
assumption of popular quenching models, namely that clusters are assembled from
an unbiased subset of infalling field galaxies. If confirmed, this would imply
that such models must necessarily fail at high redshift, as indicated by recent
observations.
