Paul wrote much to Timothy concerning leaven. First Timothy 1:3-4 says, "As I besought thee to abide still at Ephesus, when I went into Macedonia, that thou mightest charge some that they teach no other doctrine, neither give heed to fables and endless genealogies, which minister questions, rather than godly edifying which is in faith: so do." Here Paul considers other doctrines, fables, and the genealogies as leaven. Then verses 6-7: "From which some having swerved have turned aside unto vain jangling; desiring to be teachers of the law; understanding neither what they say, nor whereof they affirm." Desiring to be a teacher is a kind of leaven. If you teach something that you do not know, that teaching is also a kind of leaven.
Then we go to 4:1-3: "Now the Spirit speaketh expressly, that in the latter times some shall depart from the faith, giving heed to seducing spirits, and doctrines of devils; speaking lies in hypocrisy; having their conscience seared with a hot iron; forbidding to marry, and commanding to abstain from meats, which God hath created to be received with thanksgiving of them which believe and know the truth." Surely all of these items are leaven.
In 2 Timothy 2:16-18 Paul says, "But shun profane and vain babblings: for they will increase unto more ungodliness. And their word will eat as doth a canker: of whom is Hymeneus and Philetus; who concerning the truth have erred, saying that the resurrection is past already; and overthrow the faith of some." What a leaven this is! They were teaching that the resurrection was already past, and that there would be no more resurrection. Then verse 20 says, "But in a great house there are not only vessels of gold and of silver, but also of wood and of earth; and some to honor, and some to dishonor." No doubt the vessels of wood and of earth to dishonor are a kind of leaven.
Now let us read 2 Timothy 3:5-9: "Having a form of godliness, but denying the power thereof: from such turn away. For of this sort are they which creep into houses, and lead captive silly women laden with sins, led away with divers lusts, ever learning, and never able to come to the knowledge of the truth. Now as Jannes and Jambres withstood Moses, so do these also resist the truth: men of corrupt minds, reprobate concerning the faith. But they shall proceed no further: for their folly shall be manifest unto all men, as theirs also was." Surely the corrupt minds, reprobate concerning the faith, are leaven. "But evil men and seducers shall wax worse and worse, deceiving, and being deceived" (3:13). The evil men and seducers are leaven. Then 4:3-4 says, "For the time will come when they will not endure sound teaching (lit.); but after their own lusts shall they heap to themselves teachers, having itching ears; and they shall turn away their ears from the truth, and shall be turned unto fables." The word "sound" actually should be "healthy." They will not endure healthy teaching. The desire to hear some teaching is a kind of leaven. To have itching ears is a kind of leaven.