  The Tully-Fisher relation (TFR) links the stellar mass of a disk galaxy,
$M_{\rm str}$, to its rotation speed: it is well approximated by a power law,
shows little scatter, and evolves weakly with redshift. The relation has been
interpreted as reflecting the mass-velocity scaling ($M\propto V^3$) of dark
matter halos, but this interpretation has been called into question by
abundance-matching (AM) models, which predict the galaxy-halo mass relation to
be non-monotonic and rapidy evolving. We study the TFR of luminous spirals and
its relation to AM using the EAGLE set of $\Lambda$CDM cosmological
simulations. Matching both relations requires disk sizes to satisfy constraints
given by the concentration of halos and their response to galaxy assembly.
EAGLE galaxies approximately match these constraints and show a tight
mass-velocity scaling that compares favourably with the observed TFR. The TFR
is degenerate to changes in galaxy formation efficiency and the mass-size
relation; simulations that fail to match the galaxy stellar mass function may
fit the observed TFR if galaxies follow a different mass-size relation. The
small scatter in the simulated TFR results because, at fixed halo mass, galaxy
mass and rotation speed correlate strongly, scattering galaxies along the main
relation. EAGLE galaxies evolve with lookback time following approximately the
prescriptions of AM models and the observed mass-size relation of bright
spirals, leading to a weak TFR evolution consistent with observation out to
$z=1$. $\Lambda$CDM models that match both the abundance and size of galaxies
as a function of stellar mass have no difficulty reproducing the observed TFR
and its evolution.
