Lyric discussion by anotherme 

Cover art for Finally Found lyrics by Late Night Alumni

Beautiful song! But I agree, it's sort of confusing. My interpretation is that you can go after something that makes you happy, but you can end up with an alternative that you've always been happy with as well. Here's why I see this:

The song starts off with the narrator who is having feelings for this someone, which we can see from the opening lines. Then comes the chorus, which I had to read over a few times but I understand it to mean exactly what I've written above: you go after one thing, but end up with another. Both things make you happy.

When the narrator suddenly realizes s/he wants this person to accept his/her affections (I know what I want and suddenly it's the sound of you off to the side saying, I'm finally found.) It seems as if the narrator gets what s/he wanted. Then these lines of the song come:

I hear your heart beating faster But I'm unclear on what you're after.

The relationship happens when the other person falls in love with the narrator, but the narrator can't figure out what this person wants out of the relationship. The narrator doesn't think s/he did anything wrong in the relationship but breaks-up, because s/he doesn't see a good reason to stay. (You give me no reason why I shouldn't say goodbye. I can't think what I could have said so I'll break your heart instead.)

Then we get the chorus again.

The narrator wanted this person at first, and the person did fall in love with the narrator, but then the narrator decides nothing is really happening in the relationship and there's no point to it. The narrator simply calls it off, breaking this person's heart, because they were always just as happy being single too

My Interpretation