翻譯：那就是他們都反對這個計劃的原因。
解釋：the reason why/that的區別如下：
1. the reason why其後引導的是定語從句，且該定語從句缺少壹個原因狀語for the reason.
如此題：why they are all against the plan
= for which they are all against the plan
= they are all against the plan for which
= they are all against the plan for the reason
2. the reason that其後引導的也是定語從句，但是該定語從句不缺原因狀語，只缺壹個the reason做其主語/賓語/表語等名詞形成分。
如：I don't believe the reason (that) you explained to me just now.
其中：(that) you explained to me just now
= you explained (that) to me just now
= you explained (the reason) to me just now
3. 不過在壹些非正式場合中，the reason why也可以寫成the reason that
原因：非正式用語中，關系代詞that可以代替關系副詞when/where/why，甚至可以省略不用。
4. 所以，如果此題沒有選項C，則B也可以。
但是需要提醒樓主的是，此種用that代替when/where/why只能用於少數特殊句型或口語中，壹般考試的時候，還是以關系副詞為佳。