[Coda]

"dare mo" = "everyone", not "someone" (you're confusing it with "dare ka", like the "nani ka" earlier in the lyric).

So I parse that more as "If you lose something so that you can gain something, then everyone will be hurting." In other words, it's saying that no one benefits when you have to make a trade-off.

Remember, while 「Xて、Y」 literally translates to "X, and Y", it's stronger than just the two things happening -- it implies a connection between the two things. The most frequent meaning is "X is how Y happens", either as a cause or as a means. So for example, 歩いて行く(aruite iku) is "going by means of running", and (*thinks of an example*) 食べ過ぎて死ぬ (tabesugite shinu) is "dying from eating too much".

And then there's "X and Y happen together as one thing"; for example, 食べて飲む (tabete nomu) is "eating and drinking".

Less common but not unusual is "X is followed by Y"; for example, 食べて寝る (tabete neru) is "eating, then sleeping". But even in this case there can be the implication that you're sleeping BECAUSE you ate.

As you can see it's all pretty closely related, so even if you don't know the exact context you should be able to figure out what's intended.