When 2nd Timothy 4:1-5 states that they will heap up teachers who tell them what they want to hear who do you think that the scripture is talking to? It is not talking to the unbeliever that doesn't want to stand in front of a teacher who is teaching them anything in regarding the Bible. It is talking to the other believers, you, me us. Can you hear the urgency from Paul to Timmy? Listen for it:
II Tim 4:1-5 - 4 I charge you [a]therefore before God and the Lord Jesus Christ, who will judge the living and the dead (this is the believer and unbeliever) [b]at His appearing and His kingdom: 2 Preach the word! Be ready in season and out of season.
And to think I was just going to sail right by this scripture. So Paul is saying to Timmy hey man preach the gospel whether you feel like it or not, whether it is raining or snowing, and/or whether you are speaking as a young believer to a mature audience or young Christians.