Here's another: The idea presented in the video about similarity relations being the analogous to the spatial relationship of closeness or distance can't be right.

note: It's actually hard to tell exactly what he's getting at because he says that in the nonphysical world there are no distinct things. But then he goes on a few seconds later to posit the thesis that if things in the nonphysical world are similar then they are close and if they are dissimilar then they are distant. And if they are completely similar then they are "bonded" together. Of course this is an inconsistency because unless you have distinct things there can't be any relationship of dissimilarity between different things. And if you don't have distinct things you can't have "bonded" things. So, that's another problem. Perhaps he's making use of some distinction between 'object' and 'thing', which will help the immediate inconsistency, but gives rise to other inconsistencies; but it doesn't matter for the purposes of the argument below.

Anyway, here's the argument: There are no such thing as objective similarity. Similarity is context sensitive. Distinct things may be similar in certain respects and not others. But there is no similarity simpliciter. Whether the claim that something similar to another is true depends on the context in which the claim of similarity is made. The claim that A and B are similar is really elliptical. It's the claim that A and B are similar in some salient respect. This is why those SAT analogy questions gave you two sets of things, even though an analogy is a similarity relationship between two things. The first set of things given on an SAT analogy question sets the context for you to be able to answer the second set.

I don't think that this guy really wanted to make the claim that whether two things are close or distant is a context sensitive notion - that whether it's true that two things are close or distant is a matter of the context in which the statement is uttered. One of his mistakes is to not think deeply enough about what similarity is.