N1
こそすれ〜ない
And certainly not, But certainly not, But, Although, Even though
運動は健康のためにこそなれ、絶対に損にはならない。
Exercise can only do your health good; it will never do you harm.
Explanation
「Vこそすれ、〜ない」 means 'it may well ..., but it certainly will not ...'. The two verbs are opposites. The speaker grants that the first may happen or even get worse, and flatly says the opposite result will not: 「景気は悪化こそすれ、回復はしない」 (The economy may get worse, but it won't recover), 「白髪は増えこそすれ、減ることはない」 (Gray hair can only increase, never decrease), 「感謝こそすれ、恨むことなど毛頭ない」 (I feel gratitude, and certainly no resentment at all). It is formal and used in editorials and essays.
Mixed up with
The test point is the opposite pair: the two verbs always have opposite meanings, e.g. 増える/減る, 悪化する/回復する, 感謝する/恨む.
The correct forms are 「〜こそすれ」, 「〜にこそなれ」 and 「〜こそあれ」; 「×〜はすれ」 is not used.