以上句子没有问题，只是侧重点不同，一个为特指，一个为泛指。

(1)Who is able to be egotistical needs to be strong too.

=The person who is able to be egotistical needs to be strong too.

有能力的任性的那个人也需要坚强。

(2)Whoever is able to egotistical needs to be strong too.

=Anyone who is able to egotistical needs to be strong too.

凡是有能力任性的人也都需要坚强。

(1)who引导的主语从句属于特制:who=the person who

(2)引导的主语从句属于泛指：whoever=anyone who

就像：what, whatever引导主语从句一样

(1)What she did yesterday is right.（特指对象）

=The thing that she did yesterday is right.

她昨天做的那件事情是对的。

(2)Whatever she does is right.（泛指对象）

=Anything that she does is right.

她做的任何事情都是对的。

Who is able to be egotistical needs to be strong too.是正确的句子。

以下内容摘自《牛津英语用法指南》第三版：

    在较古老的英语中，who 的用法和 what 差不多，相当于名词+关系代词，意思是the person who,whoever 或 anybody who。这种用法在现代英语中很少见。

    Who steals my purse steals trash. 谁偷我的钱包就等于偷了垃圾。（莎士比亚：《奥赛罗》）

    （现代英语的说法：Whoever / Anybody who ...）

【建议】因为这种用法在现代英语中很少见，所以，考试中最好避免使用。应该尽量使用现代英语的说法：Whoever / Anybody / Anyone who ...，否则可能被扣分。

同意黎老师和曹老师分析。现代英语几乎已无人再这样用了，建议不要模仿。这种用法主要见于成语、谚语或格言。又如：

Who holds the purse rules the house. 有钱就有势。

Who knows most says least. 懂得最多的人，说得最少。

Who loseth liberty loseth all.失掉自由便失掉一切。

Who lives by hope will die by hunger.靠希望而生，必因饥饿而死。

Who makes everything right must rise early.要想事事都做好，必须每天起得早。