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I did not make the claim that Darwin said first life must come from pre-existing life. In fact, I have repeatedly said that Darwin did not posit a theory for abiogenesis v biogenesis.

So far, so good.

On the other half however, if Darwin's theory allows for life (other than first life) coming from non-life - then the tree is not fully connected; it is not "whole."

You may, if you like, picture the tree floating a bit above the ground, due to lack of current information about the base. (A better image would be to have the base represented by dotted lines going to the ground, because there had to be something there.) We don't know the ultimate base of the tree, because the origin of the first life that begins the tree is unknown. But from that point forward, life begets life, and it's all descended from that common (but unknown) origin -- thus the tree diagram. We shouldn't be having such difficulty over this.

In fact, it is not a tree at all, but a field of grass.

Not at all. Unless there were multiple episodes of non-living material developing life, each leading to an independent line of descent. But then, we wouldn't be able to observe, as I believe we do, that everything seems to be related. So it's not a field of grass. Just one tree.

The evolutionary tree of life, common descent, relies on "life begets life" in order for it to be a continuum.

Yes, after the first life has begun -- and I suspect it began from non-living organic material -- all subsequent branches and twigs on the tree are begotten from earlier life.

If we're still in disagreement, please let me know where.

Thank you for your reply!

Unless there were multiple episodes of non-living material developing life, each leading to an independent line of descent. But then, we wouldn't be able to observe, as I believe we do, that everything seems to be related. So it's not a field of grass. Just one tree.

That is the point. One cannot say it is a continuum - a “tree” - in the face of the possibility of multiple episodes of abiogenesis or biogenesis.

That life is a continuum was the theory of evolution. The previous thinking was that it was not a continuum. No omne vivum ex vivo, no continuum.

That everything seems to be related doesn’t satisfy because nothing precludes the abiogenetic or biogenetic episodes from being the same or similar.

Of course, if there is no continuum then half of the dispute with Young Earth Creationists goes away. So that part would be a good result.