As must everyone, for as we negotiate the curves and corners of our lives, we must continually give up parts of ourselves. 

将as must everyone移至句末，就好理解了。

For as we negotiate the curves and corners of our lives, we must continually give up parts of ourselves, as must everyone.

For为并列连词，偶尔用于句首，用作连接性状语，表示本句是对前一句的原因。这种用法类似于大写的And，But, Or开头的句子。例如：But I don't believe him.

as we negotiate...our lives 为时间状语从句 。

we must continually give up... 为主句。

as must everyone 为比较分句，分句采用倒装语序。意为：就像每个人都必须这样做那样。must 替代了must continually give up parts of ourselves. 如果不倒装，则as分句为：as everyone must (do).