why didn't the putnams like the Nurses?

There are several reasons why the Putnams would want to see Rebecca Nurse done away with. For one thing, the Putnams and the Nurses were in a disputer over the ownership of a piece of land.

Another reason why the Putnams would dislike her is that she spoke out against hiring their friend Rev. Parris to be pastor of the church. Note that it was their daughters, Betty Parris and Ruth Putnam, who first had the "spells" and that their parents were the first to mention witchcraft.

The biggest reason why Goody Putnam hated Goody Nurse was because of something she said about Ruth and Betty. Goody Putnam asked Rebecca to go to Ruth and try to wake her up. Rebecca tells her that her experience of being mother to 11 and grandmother to 26 tells her that the girls are just playing a silly game. That cuts Goody Putnam to the heart because almost all of her children have died. Rebecca's reminding her of how many living children and grandchildren she has feels like an insult to Goody Putnam and makes it easy for her to start suspecting that her babies died of unnatural causes, and maybe it was Goody Nurse behind them.