This seems to be a common reason to decide against breastfeeding.
Here are some ideas:
Some people see feeding as a major way of bonding, and they
don't want their mate (or whoever) to miss out on the opportunity.
There are many ways to bond with baby: diapering, bathing,
massage, cuddling, rocking, singing immediately come to
mind.
The baby's father (or grandmother, brother, sister, other
mother...) is not just an inferior mother substitute.
These people can bond with the baby without depriving her
or him from the best food and
best preventive medicine available.
In fact, if they really care for the baby, they would never
think about doing otherwise.
As for the issue of feeding and bonding, the feeding aspect
of breastfeeding probably plays a relatively minor role in
bonding to begin with. It's the cuddling, skin-to-skin contact,
smells and vocalizations, eye-to-eye contact that play the
major role. See the page on the psychological benefits of
breastfeeding for details.
All these are available to a non-feeder too!
You should, however, accept that babies need to form one
primary bond in early life, and this is usually and preferably
with the mother.
The best way the mother's mate can form a good relationship
with the baby (and keep one with the baby's mother) is to
support and help them in their breastfeeding relationship.
Soon, the mother's mate will form a relationship with a
baby that's different (yet equally fulfilling) from the
mother's relationship with the baby. Usually, this other
relationship will be based more on stimulation, while the
relationship with the mother is based more on comfort.
Some people want to use bottles so someone else can feed the
baby at night.
If you bottle-feed, you need to spend time warming a
bottle. By this time your baby might be screaming, and you need
to pace the hallway to calm her or him enough to eat. Everyone
will be awake and the baby will swallow too much air and need
to be burped...
If you breastfeed, all you have to do is turn on your side
and latch the baby on. The baby probably won't even start
crying. You'll drift back to sleep soon. In fact, you'll sleep
better because the hormone prolactin that your body produces
during nursing has a relaxing effect.
Some people want to bottle-feed so the mother gets a break
from the baby every now and then.
This is usually a trap. Most bottle-fed babies are fed
almost exclusively by their mother.
The mother ends up doing more instead of less work
that way: if you breastfeed, all you do is sit (or lie) down
and attach your baby to your breast. If you bottle-feed, you
have to shop for formula, bottles, nipples, bottle brushes,
sterilize bottles and nipples, mix formula, and warm bottles.
It also costs more.
This may also hurt your baby. In addition to the health,
nutritional, and psychological
advantages of breastfeeding that your baby is missing out on,
there is an additional danger. In the early stages of life, a
baby needs to form one primary bond (normally with the mother),
and also needs a small number of permanent care takers.
Changing caretakers often puts the baby in stress (even adults
are stressed out when they have to keep forming temporary
relationships with new people all the time).
Some people choose to bottle-feed so the mother can be away
from the baby for extended periods (usually to go back to work),
and other people can feed the baby.
See the page on going back to
work. Most people can combine breastfeeding with work. You
might need to supplement with
formula (depending on the baby's age when you return to work
and the nature of your workplace), but you should not give up
on breastfeeding altogether.