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That would have been contrary to who he was as a character and contrary to the message of nonconformity the film promotes. He wasn't a coward, he was a kid who saw no way out of the plan his father had set for him. It's easy to say as an adult that there are options, but as a kid, you don't really see options or a way out. And even as a kid, he knew nothing would change his dad's plan - not a talk from a teacher, not his own words or actions, not even his mother's help; not that she was offering any. And so in his child's mind, the only way he knew to escape his fixed life was to become a true dead poet.

Neil wasn't a coward, he was a sensitive boy of 17 pressured & browbeaten by his father, who saw Neil only as a way to fulfill his own thwarted dreams of youth. Neil was going to be all the things that his father had wanted to be; Neil as an individual human being didn't really exist for him. So Neil knew very well that his father would never agree to such a meeting with Mr. Keating.

No, Neil was NOT a coward. He was trapped, as he stated to Mr. Keating with a despairing laugh, and he saw no way out, because had inflicted such emotional damage on him for those short 17 years of his life. And in 1959, outside options & help were practically non-existent. The culture that maintains schools like Welton would have backed his father 100%. All of the circumscribed world that Neil knew would have done the same thing to him.