TWO roads diverged in a yellow wood, ...
[Road "First", aka "Scary Road"]
And looked down one ... To where it bent in the undergrowth; ...
[Road "Other", aka "Happy Road"]
Then took the Other, as just as fair,
And having perhaps the better claim, ...
Oh, I kept the First for another day!
In other words, "I didn't take the First road; I took the Other road."
Substituting, this brings us to, "I didn't take the Scary Road; I took the Happy Road."
Then, the key is...
Though as for that the passing there
Had worn them really about the same, ...
This means "both roads were equally traveled". So therefore we must extrapolate into the future. Take a thousand average people. Not entrepreneurs; think more along the lines of Grandma. Now show them a Scary road and a Happy road, then ask them to choose. Which one are they more likely to select?
I'd say the Scary road is the one "less traveled".
I shall be telling this with a sigh, ...
Why would he sigh if he were not lying?
Two roads diverged in a wood, and I—
I took the one less traveled by
This means he claimed to have taken the "less traveled" road, which is the Scary road. But he took the Happy road.
Why would the first road be "scary" and then the other be "just as fair"? "Fair" is a positive description.
If both roads are just as fair as each other, there isn't one scary one and one happy one, there's either two scary ones or (more likely) two happy ones.
Anyway, shouldn't it be ONE road diverged in a yellow wood? If TWO roads diverged, that would make four.
The poem is about a man who, "years and years hence", will be remembering his life, and up there near the top of his memories to tell people about is how he chose which of two almost identical paths he took when walking in a wood, once, and they were roughly the same. Does that sound like the sort of memory someone who would pick a scary road would choose to reminisce about? Does it sound like the sort of tale a habitual liar would tell? No to both. It sounds like the sort of tale a really boring person with no interesting memories would tell.
He was walking through a wood, not trying to get anywhere in particular and not caring where he went. It was probably quite pleasant, and it wasn't the hundred acre wood or the Lord of the Rings evil forest, both roads came out the other side of the wood and then he went home.
"Less traveled by" could mean (1) less traveled at the time he made the decision or (2) less traveled at the (later) time when he's telling the story. I think #1 is the obvious meaning; your argument depends on taking it to mean #2.
As for "Why would he sigh if he were not lying?", I hardly know what to say: what do sighing and lying have to do with one another? He expects to feel some regret, some sense of a missed opportunity, at never finding out what was down the path he didn't take. At least, that's my reading and it has the advantage that regret does sometimes make people sigh, whereas lying doesn't.
Substituting, this brings us to, "I didn't take the Scary Road; I took the Happy Road."
Then, the key is...
This means "both roads were equally traveled". So therefore we must extrapolate into the future. Take a thousand average people. Not entrepreneurs; think more along the lines of Grandma. Now show them a Scary road and a Happy road, then ask them to choose. Which one are they more likely to select?I'd say the Scary road is the one "less traveled".
Why would he sigh if he were not lying? This means he claimed to have taken the "less traveled" road, which is the Scary road. But he took the Happy road.Therefore, the poem is about a lie.