There's a difference between positive "rights" and negative rights.
>The state tells me I have to sign up for the draft and pay taxes
Yeah, they curtail your rights in order to provide for the common good.
>why can't it tell a 16 year old girl she has to fuck me
It can (ignoring constitutional limitations, legislative feasibility, etc.). It's the same as for stuff like food and healthcare; sure it's nice to say everyone deserves it, but if you can't acquire it on your own then your rights aren't being violated. Rights are traditionally considered within what the government can not do to you, i.e. they can not imprison you without due process, take away your guns, or prevent you from speaking/praying.
Of course idiots (read: leftists) misinterpret the entire notion and start trying to declare goods and services rights, so you get banana republics where everything's a constitutionally enshrined right but for some reason the economy's in shambles with 200% inflation and it's clearly America's fault for not helping enough and/or interfering too much.