What is Robert Frost 'owning' in these lines?

Question

I read the poem "A Roadside Stand" by Robert Frost, and I have accumulated a few questions through the poem. So, I will be posting some questions from the same poem, if you can please answer my other questions as well. Thanks to all :)

When Robert Frost says, "I can't help owning the great relief it would be to put these people at one stroke out of their pain", What exactly is he owning? Is he owning the 'thought' of putting people out of their pain at one stroke? or what?

I will really appreciate anyone who would give an elaborate answer.

Here you can read the whole poem. Below I have given the particular paragraph.

No, in country money, the country scale of gain,
The requisite lift of spirit has never been found,
Or so the voice of the country seems to complain,
I can’t help owning the great relief it would be
To put these people at one stroke out of their pain.
And then next day as I come back into the sane,
I wonder how I should like you to come to me
And offer to put me gently out of my pain.

Answer 1

To own, from Merriam-Webster:

transitive verb

1. a : to have or hold as property : possess
   b : to have power or mastery over
   • wanted to own his own life

2. : to acknowledge to be true, valid, or as claimed : admit 

   • own a debt

Here, it's not used in the first sense, but in the second.

Frost is saying that he can't help but admit that there is great relief in being able to put these people out of their misery. However, when he comes to his senses, he considers how he would feel if someone were to offer the same for him ... which is arguably more than what he would offer to those people — a choice.

Answer 2

As @muru described, owned has two meanings. The more familiar meaning denotes possession, but there's a less common secondary meaning of "admitting something is true," sometimes used in the construction "own up (to the truth)."

Frost is using the term primarily in the second sense, but with strong connotations of the first. In other words he is both admitting to his shameful thought and taking responsibility for his possession of it.

As to why the thought is shameful: "Put out of their pain" may sound benign, but it's a euphemism for euthanasia ("mercy killing"). So he's suggesting it would be better to kill the rural poor than let them continue living their miserable lives --a postively Hitlerian solution to their "problem." In the next breath however, he extends a little more empathy and imagines them suggesting that he be the one to be put out of his misery (mercy killed) instead.