I got hung up on that question as well, and so have many other people, especially critics like Bortkiewicz. It isn’t helped by David Harvey in his book saying that it is a “cryptic assertion” that the substance of value is abstract labor.

If value is an assertion, then it can be taken on faith or dismissed with as little reason.

First is recognizing that there must be a third thing if qualitatively different things, in different quantities, are compared quantitatively. In section 3 Marx cites Aristotle on this. Strictly speaking it is logically invalid to say “1 table is equal to 3 chairs” because they are different things. What is unsaid in that statement is “some common substance/property between 1 table and 3 chairs is present in equal quantity”. So it implies both qualitative equivalence (same substance) and quantitative equivalence of some third thing.

At this point it’s unclear why Marx singles out labor… let’s see what he thought about this “cryptic assertion”:

If the substance of value being labor was a speculative assertion, then someone else could suggest something else common to all commodities (and many have) such as that they all contain energy, or they are all abstractly useful.

But labor being that common thing is not speculation, it is a prerequisite for a society in which there is a division of labor among independent producers, where exchange of products mediates the exchange of private concrete labors.