  Gravitational-wave observations of binary black hole (BBH) systems point to
black hole spin magnitudes being relatively low. These measurements appear in
tension with high spin measurements for high-mass X-ray binaries (HMXBs). We
use grids of MESA simulations combined with the rapid population-synthesis code
COSMIC to examine the origin of these two binary populations. It has been
suggested that Case-A mass transfer while both stars are on the main sequence
can form high-spin BHs in HMXBs. Assuming this formation channel, we show that
depending on critical mass ratios for the stability of mass transfer, 48-100%
of these Case-A HMXBs merge during the common-envelope phase and up to 42%
result in binaries too wide to merge within a Hubble time. Both MESA and COSMIC
show that high-spin HMXBs formed through Case-A mass transfer can only form
merging BBHs within a small parameter space where mass transfer can lead to
enough orbital shrinkage to merge within a Hubble time. We find that only up to
11% of these Case-A HMXBs result in BBH mergers, and at most 20% of BBH mergers
came from Case-A HMXBs. Therefore, it is not surprising that these two spin
distributions are observed to be different.
