He did. The New Testament couldn't really be much more explicit.
It isn't explicit; there's a lot of assumptions going on.
"Paul said, 'I do not allow a woman to speak or to snatch authority from a man' - that must mean that women can't preach, because it involves speaking, or be ordained because that would mean being in authority over men'. " What Paul did not allow, must be a command from God.
If it ever was, then clearly God's changed his mind since then. And Jesus did not teach it at all.
Not over this issue we wouldn't.
Or are you saying that even if Jesus HAD said, "I forbid any woman to have a leadership role in my church - anywhere, ever", there would still be women who went for it, and there would be male clergy who were disobedient enough to let them?
Does Tradition outweigh it?
Traditions can change.
Once, God's people set up stones/altars in special places if God had met them there - Abraham, Isaac, Jacob.
Then the tabernacle was built with the Ark of the Covenant, and if ever that ark was captured, Israel were in trouble; it was where God "lived".
Then the temple was built, and all the feasts and sacrifices took place there; it was God's house.
Now he lives in us; we are temples of the Holy Spirit.
Traditions can also be wrong; just because someone has done something for many years, it doesn't mean it is/was right. Look at the Middle ages - drowning people for being witches, when today we might say that they had the gift of healing or a word of knowledge from God. People used to talk about the gods throwing the furniture around - today we can describe a thunderstorm scientifically.