The specific scenario in question is an arcane bloodrager getting the free buff spells when entering his bloodrage at 4th level or higher. The bloodrage itself is supernatural and does not provoke, but how does that work with arcane bloodrage being a spell like ability?
Arcane Bloodrage (Sp) At 4th level, when entering a bloodrage, you can choose one of the following spells and apply its effects to yourself: blur, protection from arrows, resist energy (choose one energy type), or spider climb. These effects last for as long as you continue bloodraging, regardless of the spell's normal duration.
Under spell like abilities it says
Using all other spell-like abilities is a standard action unless noted otherwise, and doing so provokes attacks of opportunity.
My DM believes that this means if I enter a bloodrage and choose to have one of these spells affect me, I'd be provoking an attack of opportunity. I believe that since I'm not using a spell-like ability as a standard action, it does not provoke. I can't find anything in the rules one way or another.
Best Answer
Your DM is correct: it does provoke an AoO.
The confusion here comes from your reading of the sentence where you believe that the second part only applies if the first is true. The sentence is in fact a two item list; the first half and second half do not interact with each other in any way.
The d20pfsrd also says
And spells provoke (except when cast as a swift action).
Interesting, you can Arcane Bloodrage defensively, since you have not actually entered a bloodrage when you apply the effect, it is done as part of the activation.
This is the RAW on the matter. The fact that swift action spells do not provoke does not mean that free action spells or spell-likes do not, though it is certainly worth making that point when discussing this with your DM. (Especially since the reason is that there are no free action spells any more is, to the best of my knowledge, because when pathfinder came out it had turned them all into swift actions)