Present wishes indicate something that is "contrary to
fact." That is, wishes are something that is untrue but
desired. For example,
I wish that I had a sports car.
(The truth is I don't have a sports car.)
I wish that I were a doctor.
(I'm really not a doctor.)
For present wishes, the past tense is used in the that
clause, because it indicates a situation that is only
imagined. Sometimes the word that is omitted.
She wishes (that) she had a diamond ring.
He wishes (that) he were rich.
To express possibility (can) and future intention (will),
use the modals could and would respectively.
She wishes that she could sing.
They wish that she would stop.
When a "be" verb is required, the word were is used,
regardless of the subject.