> I always assumed that sign language was taught after reading and writing.

Sign languages are often people's first language. If you're like me, you probably learned english as a toddler through magic and were later enrolled in school where you refined your spoken and written abilities. For many deaf children english is a second language.

For children born deaf, sign language can be (and should be) their first language. It turns out, incidentally, that a baby’s ability to form signs comes earlier than their ability to vocalize, even for hearing children, so there are benefits for using sign language even with hearing children. My children learned some basic signs as infants (water, bathroom, more). I really need to get on the ball about learning ASL properly (and my family as well since they’ll need it just as much as me) since my cochleae are on an ineluctable road to deafness and at some point, maybe ten years, maybe thirty, maybe never, I will be unable to hear instead of being merely hearing impaired.

> I always assumed that sign language was taught after reading and writing.

Basically, you're saying "I always assumed that speaking was taught after reading and writing." (which can happen, but is far from being the norm)