I can remember having a range of books and sitting down eagerly to read with ds circa 15-18 months (when he started to have a mind of his own in other words) and he shoved my arm away!
Eventually chose a book with a tractor on the front and then refused to let me turn the page because there was a tractor on the first page and not the second 
DD is a similar trajectory. For a while she just used to enjoy pulling books out and putting them back. Sometimes if I suggest reading she refuses. She absolutely will not read a book she doesn’t want to. Reading often isn’t something you can ‘just do’, especially with toddlers, it has to be built up and part of life (which is why I’m not a fan of the ‘bedtime story’ - keeping books solely for the part of the day parent and child are most tired and stressed doesn’t make sense to me. I don’t mean don’t read with them then but it shouldn’t be the only time you read, if that makes sense.)
It’s a bit like the potty training thing on here. For whatever reason some posters delight in believing that the country has gone to the dogs and it is filled with lazy parents who can’t be bothered to read or potty train their child and it isn’t that, or mostly isn’t that. It’s more to do with how that environment is created.
Now I’m going to see if my two year old wants to read Mog and the Baby for the 10000th time …