What is the core problem with false doctrine? False teaching is destructive (2 Pet. 2:1), but that is a result. It is empty (Matt. 15:9) but that speaks to quality. False doctrine is of the Devil (2 Cor. 11:3-4; 13-15), yes, but that has to do with origin. At its heart, the primary issue with false doctrine is that it denigrates the Cross of Christ.
Consider Galatians 5:1-2,
Stand fast therefore in the liberty by which Christ has made us free, and do not be entangled again with a yoke of bondage. Indeed I, Paul, say to you that if you become circumcised, Christ will profit you nothing.
False teachers in Galatia sought to proselytize gentile Christians by binding portions of the Law of Moses upon them (cf. Acts 15:1-5). They preached “another gospel” (Gal. 1:6-10) motivated by their own desire to avoid persecution for the cross (Gal. 6:12). But their false gospel robbed the Galatian Saints of their “liberty” and severed them from Christ.
The message of Galatians is that Christ plus anything equals nothing and Christ plus nothing equals everything. To substitute the gospel of Christ with the doctrine of the Judaizers, or any other false doctrine, is to make the Cross “of no effect” (1 Cor. 1:17). All that Christ accomplished on the Cross– the salvation of the soul–is made void by any doctrine that pushes us away from Him (1 Tim. 1:3-11), and causes us to be lost.
It is not uncommon to find a person willing to play fast and loose with the doctrine of Christ. Such a one should remember the eternal importance of the Cross.