Why should a firm outsource anything?

From an economic standpoint, a firm should outsource any non-core activity if it can be done by someone else for a substantially lower price. This is more effective use of the firm's resources which makes it more competitive, and therefore represents the best interests of employees, shareholders, creditors etc.

Outsourcing work usually increases the cost of managing the work, and also the risk of failure. If the outsourcing involves a 3rd party directly interacting with the firm's customers, this is also a further risk.

Before deciding if outsourcing is a good idea, these additiona risks needs to be considered, not just dollar pricing.