Summary: Many will reject the sound doctrines of the bible to have their "Itching ears" satisfied. They will seek out teachers and preachers to make them feel good about themselves and to have their sins justified.
Yesterday on Facebook, a quote from A.W. Tozer popped up (I follow the “A.W. Tozer - Daily Inspirations from Great Christians” FB page). It so much applied to today’s message:
"A whole new generation of Christians has come up believing that it is possible to “accept” Christ without forsaking the world." 
In today's world, you cannot tell the difference between many so-called Christians and the rest of the world. James, in his little letter, made a statement about being a friend of the world:
James 4:4 (NKJV) Do you not know that friendship with the world is enmity with God? Whoever therefore wants to be a friend of the world makes himself an enemy of God.
Yet the world tries to convince you otherwise. Today’s passage, in a larger context, is Paul giving final instructions to young Timothy. Here is the catch, Paul spends a lot time in his many letters warning about false teachers, but in today’s passage, Paul is warning Timothy about inclination of the audience for error.
2 Timothy 4:3–4 (NKJV) For the time will come when they will not endure sound doctrine, but according to their own desires, because they have itching ears, they will heap up for themselves teachers; 4 and they will turn their ears away from the truth, and be turned aside to fables.
ILL. On April 14, 1865 (the same day he was fatally shot by John Wilkes Booth) Abraham Lincoln signed legislation that would allow for the creation of the Secret Service—not to serve as presidential bodyguards ( In 1901, the agency was asked to begin its protective mission after the assassination of President William McKinley), but to help suppress money counterfeiting. Treasury Secretary Hugh McCulloch came up with the idea after Lincoln called for a commission to help stop the counterfeit money, which at that time was estimated to account for between one-third to one-half of the American currency in circulation. To this day, the Secret Service plays a role in creating new methods to fight against counterfeit bills, including training law enforcement operations to catch counterfeiters, investigating and apprehending criminal organizations and individuals, and raising consumer and business awareness about fake bills.
How do these federal agents train to spot counterfeits? Not with counterfeit money, but with the real thing. They know the real things so well inside and out. The feel, the markings, the watermarks the security strip. They know all aspects of the genuine article so well that when they encounter the false, it is obvious to them. POINT – the best way to decide if something is counterfeit is by handling and becoming familiar with the real thing. 
In cults (Mormons, Jehovah Witnesses, plus other outlandish cults), as well as followers of the many health, wealth and prosperity preachers, many of their recruits are from Baptist churches.
Why? Because people do not know the real thing. Many do not know what they believe, they do not know the word of God, they are not familiar with the basic doctrines that the Bible teaches, they quickly fall for false teachers who miss-use scripture to tickle the ears, to appeal to the sinful nature of people. Here is the problem of the greater church today.
2 Timothy 4:3a (NKJV) For the time will come when they will not endure sound doctrine,
The time is coming and time has come. It is today. “They” in the verse is not talking about the world, “they” is referring to the church! Here is the world we live in:
1 Timothy 4:1–2 (NKJV) Now the Spirit expressly says that in latter times some will depart from the faith, giving heed to deceiving spirits and doctrines of demons, 2 speaking lies in hypocrisy, having their own conscience seared with a hot iron,
Falling from the faith because they were never firm in the faith. They never knew the deep doctrines of the Bible. As our culture becomes more and more anti-Christian, True Christians will stand out more and more like sore thumbs.
Please note I said “true Christians” because many so called Christians and Christian churches have fallen from the true faith. Their doctrines (teachings) have changed to reflect the values of the world, not those true doctrines of God as portrayed in Scripture.
Many preachers and churches water down the word and ignore the depth of Scripture of sound or healthy doctrines. They start with the verse and move on to some social and cultural issues. They are "tickling the ears" of their audience.
I am called to teach and preach scriptural doctrine, not just some cherry picked, pleasant, feel good, Bible stories.
The church going crowd in today’s world rejects sound doctrine: “but according to their own desires, because they have itching ears,” they are seeking out feel good messages. Why? Because their ears are itching. People are searching for teachers and preachers that will teach what they want to hear. And they (the false teachers and the feel good preachers) are out there. You can turn on your TV and search out and find the “Church of Feeling Good about Yourself.”