As a general rule, you can only use one negative in an English sentence. I don't like either one. -- negative verb + either. I like neither one. -- postive verb + neither

I want to do neither-this one seems fine to me. I don't want do it, too- This should be "I don't want to do it either". I don't want to do both of them- This one should be "I don't want to do either of them".