Because Timothy is a young man, he needs to be careful how he corrects people in the church, especially those who are older than he is. Paul also gives advice on how to care for widows. In that culture, widows were often left with no income. The church was to care for those who had no other options, but also to encourage those who could find good ways to support themselves to do so.
Paul’s advice to Timothy on correcting older people is designed for those people to accept the correction. In an ideal world, people would listen to correction no matter the age of the person correcting them. We don’t live in an ideal world though, so we would be wise to find the best possible way to correct someone so it is accepted. The goal isn’t to win, but to be helpful.