Which is more important, when contrast is present or when a second verb is used?

Question

Still struggling with this (and I can see I am not alone based on some comments, lol). Can I share my thinking and you tell me where I am making my mistake? On the quiz the question was: El policía persiguió al ladrón ________ no lo atrapó. (The policeman chased the thief but he didn't catch him. I went back and forth between "pero" and "sino que" for quite a while!  I thought "pero" would work because it makes a contrast (chased / caught). But, then I noted the change in verbs before and after "but," (persiguio / atrapo) and thus used "sino que." This issue, where I feel a note a second verb is one of the largest reasons I keep getting this wrong. How should I be approaching this differently? Thanks as always for your help! PS - I didn't use proper accents above as when I do my computer kicks me out of this program!

Inma Sánchez · Accepted Answer

Hola Terry
When you say "E I went back and forth between "pero" and "sino que" for quite a while!  I thought "pero" would work because it makes a contrast..." you're right - after you check that, you then have a look at the main clause and if there is no negation then you can't use sino/sino que. You need a first element in the negative. For example (and following this idea of the police example...), imagine that the sentence is:
"La policía no persiguió al ladrón, sino que lo dejó escapar."
Here you can use sino que because of the "no" in the first clause. And it's also seen as a "substitution" of an action so the police "substituted" the action of chasing him with the action of letting him go (instead of doing one thing, they did another thing). 
It's not an easy topic as you can see in the comments and it takes some practice. 
I hope this clarified it a bit.
Saludos
Inma