Question

she+answered+that+she+wasn't+wanting+to+come+out+to+the+pub有语法错误吗

Answer 1

没有错误，宾语从句可以使用过去进行时，表示当时她并不想去酒吧。

想说明时间是主句谓语与宾语从句谓语是同时关系，语义关系逻辑上是正确的。

Answer 2

英语中表示心理状态的动词不用进行时态。像know, realize, think, see, agree, want, remember, forget等。本句中wasn't wanting错了，因为want是表示心理状态动词，可改为she didn't want ...

Answer 3

错
want 不用进行时态

应该是
She said that she didn't want to go to the pub.