莱拉埃来？！！！！

如果非要用个that，那么这个句子应该改成
He studied hard and later became a well-know writer. That was what his father had expected.
也就是说，that 做远指，可以代替前面的句子。但是如果选A,后面句子中动词expect就少了宾语，因为that在这里只能对前面句子作照应而不能充当expect的宾语。
选择B，what就代指了前面主句说明的情况，即“他努力学习并且成为一个著名作家”，同时还可以做expect的宾语，使得整个句子一气呵成，前后照应。