Paul explained the reason for this charge next. "They" are the people to whom Timothy and his followers would preach: his listeners. In the end time they would not tolerate the truth but would only listen to speakers who told them what they wanted to hear (false doctrine, entertainment, etc.; cf. 2 Timothy 3:6). Paul pictured people who would be bored by, apathetic to, and annoyed by sound doctrine. [source][source][source]
"In other words, they have made themselves the measure of who should teach them and what teaching is acceptable." [1][source]
Moreover they would choose to believe myths rather than the truth (e.g, atheistic evolution, humanism, reincarnation, etc.; cf. 1 Timothy 1:4; 1 Timothy 4:7; Titus 1:14). The context seems to indicate that these people were believers (cf. Luke 8:13; 1 Timothy 4:1; Hebrews 3:12; 2 Timothy 2:12). Earle believed the phrase "sound doctrine" is the key one in the Pastorals (cf. 1 Timothy 1:10). [2][source]
"Timothy"s major responsibility in Ephesus was to defend and proclaim sound doctrine." [3][source]