A paradox of comparison and similarity

What is the relation between comparison and similarity?

Here is a paradox:

For philosophers like Kant, Frege and others, comparison allows us to gain knowledge about universals (properties or concepts) out of our knowledge of individuals.

Hypothesis of common sense: comparison is a bona fide epistemological process, i.e. we learn things through comparison.

But, what is to compare?

To compare is to take two things to see if they are similar (or not) and how.

Thus, what we learn from comparing things is whether they are similar or not, and how. 

Hence, before you compare two things, all you need to know about them is that they are different. 

Therefore, you can, at least in principle, compare any two things that are different.

But this would be a methodological nightmare! 

Thus, we need some heuristics to determine what things are worth comparing.

The obvious answer is that, in order for two things to be genuinely comparable they must be similar. 

But how do we know that they are similar?! Wasn’t that what comparison was for?

It seems that we have fallen into a vicious circularity where we need to know that things are similar before we compare them and learn that they are similar.

To avoid this contradiction, we must reject the hypothesis from common sense:

It seems like we cannot learn anything from comparison.

Something I realized from listening to Paolo Valore's “Ontology and Ordering Strategies: Kantian Legacy within the Quantificational Paradigm”