Yes the men should be offered because they would like time to bond with their baby also. They need time to adjust to being in a new role. The baby cries at night and sometimes the baby cries all night long who can really rest when they have a crying baby all night long.
Mothers often have a hard time in the first weeks after a child is born. They need someone by them to help them because they are often very weak. Companies should offer new fathers a short period of maternity leave. At least 2 weeks of paid maternity leave should be provided to new fathers.
There are several countries which provide family leave, for up to 3 months, including for fathers. However in the US, most companies have very stingy maternal leave, and very little paternity leave. For new fathers, it would be hugely beneficial for the entire family, newborns, and mothers to have paternity leave.
Companies should be required to offer new fathers parental maternity leave when there family has a new baby. The mother often has the right to take the time off to be with the new baby however, so should the father. This would allow fathers to spend special momments with their children.