Prophecy versus Teaching

Throughout Christian history there are two Pauline injunctions that have been used to keep women away from the pulpit:

1 Corinthians 14:34-35 (KJV)
Let your women keep silence in the churches: for it is not permitted unto them to speak; but they are commanded to be under obedience, as also saith the law. 35 And if they will learn any thing, let them ask their husbands at home: for it is a shame for women to speak in the church.

1 Timothy 2:11-12 (KJV)
Let the woman learn in silence with all subjection. 12 But I suffer not a woman to teach, nor to usurp authority over the man, but to be in silence.

But we know too well that women prophesied in the New Testament.

Philip’s daughters were prophets:

Acts 21:9 (KJV)
And the same man had four daughters, virgins, which did prophesy.

More importantly,Paul gives instructions for women prophets:

1 Corinthians 11:5 (KJV)
But every woman that prayeth or prophesieth with her head uncovered dishonoureth her head: for that is even all one as if she were shaven.

And all of this confirm Joel 2:28 prophecy of Spirit being poured on ‘sons and daughters’

So women could prophesy but couldn’t teach?
This tells me prophecy is not equal to teaching, else the question of women prophesying would never have been raised. But what is the difference between these two?

In both prophecy and teaching, men(and women) speak for God
Why would speaking for God in one occasion be forbidden and not another?

To my mind, the distinction between the two lies in spontaneity. To teach one must first apply their mind and spirit to the word of God, derive some truths which they then share with others. But to prophesy receives the word of God directly from Holy Spirit. Look at Prophet Agabus in action:

Acts 21:11 (KJV)
And when he was come unto us, he took Paul's girdle, and bound his own hands and feet, and said, Thus saith the Holy Ghost, So shall the Jews at Jerusalem bind the man that owneth this girdle, and shall deliver him into the hands of the Gentiles.

No scriptures were necessary for Agabus to speak the mind of Holy Spirit, but Peter needed scriptures to teach about Pentecost in Acts 2.

Is it possible that women were forbidden to teach because of their limited access to the written word?
If they had limited access to the then scriptures, and I hear they never went to the synagogue, they were much more susceptible to error than men.