Where did the thought process of men teaching men and women teaching women come into play. Did Jesus ever discern a difference? Shouldn’t the need be met regardless of the person's gender. I have never understood it when other Christians tell others that they shouldn’t study with someone of the opposite sex (understand you are not alone in their bedroom). I would appreciate your advice on this as well. Is it OK to have friends of the opposite sex in a dating relationship or even a marriage? As long as one is practicing self-control nothing will come of the matter.
There is nothing wrong with a man teaching a woman. If it were, then it would have been wrong for Paul to teach Lydia or Jesus the woman at the well. However, it doesn't mean we ignore the potential for problems. In both cases that I cited, the teaching was done in a public area where someone else might come by at any moment. In the case of Paul, neither he or Lydia were alone. There others with them.
When Paul wanted to have the gift gathered by the Gentile churches sent to Judea, he insisted that others actually carry the money. It wasn't that Paul wasn't trustworthy, lacked self-control, or didn't trust himself. "Avoiding this: that anyone should blame us in this lavish gift which is administered by us -- providing honorable things, not only in the sight of the Lord, but also in the sight of men" (II Corinthians 8:20-21). It is an important principle.
When teaching another person, you don't want that teaching time to be an occasion for temptation or for malicious rumors. Hence, my general rule has always been that when talking to someone of the opposite sex, I always have someone with me or the discussion takes place in a public area. In this way I protect both of our reputations and "give no opportunity to the adversary to speak reproachfully" (I Timothy 5:14).
The same principle applies to friendships. I expect people to have both male and female friends. Yet, because sin is in the world, I urge people to take precautions. It is the concept of honor and integrity that is so often overlooked. It is because a person is your friend that you take extra precautions regarding their reputation.