A 401k plan, even without any matching funds, is going to cost an employer money in HR time and administration fees.
Any business more complicated that burger flipping is also going to spend significant money on training and recruiting new employees.
From a business perspective the theory is that offering a 401K will reduce costs to recruit and retain valuable employees. Obviously a 401K plan is a great benefit to offer to potential recruits.
But perhaps just as important, many 401K plans with matching also have a vesting schedule. A common example is a 3 year even split vesting schedule. In that case, if you leave after 1 year you get to keep 33% of the employer matching funds. After 2 years, 66%, and so on.
This is a "golden handcuff" strategy to reduce turnover. The reduction is training and recruiting more than offsets the amount spent on the plan.
Finally, offering a plan is just a humane thing to do. Not sure that argument will fly at your workplace, but it's the truth :-)