The anointing

Some professing Christians quote 1 Jn 2:20,27 to disprove the need for theologians and Bible scholars. That's not confined to charismatics. Some cessationists have a folk theology regarding spiritual illumination or divine guidance in decision-making and ethical discernment that's equivalent to charismatic theology (prophecy). 

i) 1 John opens with an appeal to the author's authority as an eyewitness to the ministry of Christ (1:1-14). He taught this congregation. As the Beloved Disciple in the Fourth Gospel, he was one of Christ's chosen witnesses. 

He's not going to sabotage his own role by saying, in 2:27, that they don't need any teachers whatsoever, including the author! That would mean they don't need to read and heed his letter. It's not his intention to discredit his own teaching authority! That's utterly counterproductive.  

ii) Notice that 2:20 is followed by reminding the audience what they were already taught (vv21,24). That refers back to the instruction they originally received from the author–the Apostle John. 

What they know, what they already know, is grounded in the fact that they were evangelized and discipled by a member of Christ's inner circle. That's public, objective teaching. Reporting what Jesus said and did from a firsthand observer and confidant of Jesus. That's the standard of comparison. John's personal testimony.

iii) As one commentator notes, there's probably a play on words, between anointing (chrisma) and the Anointed One (Christos). Christians and Christ go together.

iv) Another factor is that John is writing in response to a split in the church. Some former members rebelled against John's apostolic authority. So John is reasserting his apostolic authority, as a chosen witness of Jesus. 

The point, then, is that John's parishioners don't need another teacher, a new teacher, meaning the false teachers who broke with John. Rather, they were properly taught the first time around by the Beloved Disciple. They need to remain steadfast to the original message (2:7). 

v) Finally, there may be a charismatic or pneumatic element, similar to sheep knowing their shepherd's voice (Jn 10). That, however, is not independent of John's witness.