I'm not challenging your authority as you enlightened so many ignorances of mine, but I've found many writings about conditional2, and many of them like the underlined explain that it can be either impossible(counterfactual) or improbable(unlikely or hypothetical) in the present, so in conditiona2, counterfactual doesn't seem to be the only one factor. I'm not sure.
*****some excerpt about second conditional.
Points to remember about the
Second Conditional:
- They are made up of two clauses: The “If” clause” and the “Result” clause.
- The order of the clauses can be reversed: I would buy a house if I had a million dollars.*
- The verb in the “If” clause is in the past simple tense.
- In the “Result” clause we use would + infinitive
- The second conditional is used to talk about unreal (impossible or improbable) situations in the present moment.
- Notice in the sentence “If I were you, I would try to learn English.” I used the verb were. Normally the subject “I” goes with “was.” This is an exception to the rule and both “If I was you…” or “If I were you…” are acceptable.