This isn't a common simile in English. You can probably figure it out yourself based on a literal translation, plus your best guess of what a rooster likes to do (to hens) and what it might mean to have an itch that needs scratching!
What's not clear is whether the teacher gives this to his students as an example of a simile, or has asked them to generate their own, of which this is an example. Either way round is plausible to me.
It's a simile alright, but not one that's known to me. It's meaning is readily deducible: a rooster (which is strongly associated with male sex drive), with an itch (in the sense of a strong desire or yearning). He goes to her like a rooster with an itch means that he approaches the woman with enthusiasm, in eager and hopeful anticipation of his lustful desires being met.