"reading fairy tales can teach children moral behaviour and empathy".
Oh really? Let's just look at some of these fairty tales, shall we?
1: "The Ugly Duckling." You will only gain worth when you are aesthetically pleasing.
2: "Cinderella". It is fine to form a long lasting relationship based on a few hours spent together.
3: "The Tinder Box". Murdering someone just so you can gain their possession, when they have helped you, is perfectly acceptable.
4: "Jack and the Beanstalk." Theft and manslaughter are to be applauded.
5: "The Little MatchGirl". Social responsibility towards a starving, under-dressed child can be quietly ignored as long as there's a happy ending.
As for reading to your child more and saying lots of nursery rhymes, I said and say loads of rhymes and stories to both my lads since they were born. And the lads got to hear them all as babies and toddlers and knew them back. Ds1 could recite back the story of the three little pigs before he could say "mine" or "mummy" or "no" or "duck". Ds2 can sing "twinkle twinkle little star" but not say "want juice".
Because oh yes, despite all this plethora of nursery rhymes and stories (and of course I spoke and speak to them normally as well), both of them still are on the autistic spectrum.