Did Jesus teach that everyone is a sinner because of Adam?
No. Jesus taught that all were sinners, but He did not teach the ramifications of Adam's sin or trace universal sin back to Adam. That connection was revealed later through the Apostle Paul, who explains how Adam's sin carries over into the whole human race.
Les explains that in verse 12 Paul bridges information found nowhere else in Scripture. Jesus never mentioned it, and Les suggests the reason is that He would wait for the revelations given to this apostle. Jesus never taught, as far as Les is aware, the ramifications of Adam's sin and how it carries over into the whole human race. Naturally, He certainly taught that all were sinners, but to tie it back into Adam like Paul does, no. Nowhere else in the Old Testament is it taught, but here it comes and is laid out as plain as day.
Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:
More Questions
Why didn't Jesus teach that Adam's sin affects all of us?
Jesus did not mention the ramifications of Adam's sin for the human race because He intended to wait and reveal that truth through the apostle Paul.
Does the Bible teach original sin?
The Bible teaches that there is such a thing as an original sin or the fall, contrary to those who deny it.
Are we sinners because we commit sins, or do we commit sins because we are Adam's sinful offspring?
A person is a sinner by virtue of being Adam's offspring, and then, because he is already a sinner, he commits actual sins.