。
Why can't I sing like they do?
Literal
Why I [topic-は] them [like-のように] sing [thing-こと-が] cannot [plaintive-んだ].
A plaintive question with 俺 marking rough masculine speech and frustrated self-comparison. ~のように 'like / in the manner of' uses the attributive の to link a noun to よう 'appearance, manner.' 歌うこと 'singing (as a thing)' nominalizes the verb; できる takes its object with が, and the negative form 出来ない means 'cannot.' The んだ sentence-ender frames this as explanation-seeking — 'why is it that I can't?' rather than a neutral information-request.