I suppose what you’re really asking here is why tree structure in the data is compelling evidence for common descent. Succinctly put that is because tree structure in the data is what we expect given common descent, and we do not expect it on alternative hypotheses. It should be pretty easy to see why tree structure is expected on common descent. After all, if two species derive from a common ancestor, the ancestral lineages splits into two new lineages, and if one or both of these two lineages in turn also split into two later, we get two more bifurcations and so on and so forth, and this should form a tree. If changes in characters (however they arise) accumulate independently on different branches, this should make the characters support a tree.
In logical form the argument is basically:
If X, then Y.
If not X, then not Y.
Y, therefore X.
If there is common descent, we expect there to be tree structure in the data.
If there is not common descent, we do not expect there to be tree structure in the data .
There is tree structure in the data. Only one hypothesis makes that an expected outcome, so the data de facto supports the common descent hypothesis over others.
Now whether you find that compelling is of course a matter of your own psychology.
Counter arguments have been proposed by creationists before, such as trying to conjecture that some form of independent creation would also inadvertently produce tree structure in the data. I have yet to see a creation-model that actually predicts tree structure in the data inadvertently, which does not explicitly involve actual common descent with accumulating changes on splitting branches of genealogical descent, or deliberate fakery (as in someone intentionally creates tree structure in the data despite there being no functional reason to do so).