You sure, you are not confusing activated abilities and triggered abilities? The two are quite different. Only activated ability can be activated, which will be stopped by Petrify. But triggered abilities trigger, which will NOT be stopped by Petrify. Activated abilities cannot be triggered, and triggered abilities cannot be activated.

Activated abilities ALWAYS use the template [cost]:[effect], either in the text of the ability itself, or in the rules if it is a keyword ability. If it does not have that template, you are not dealing with an activated ability.

Triggered abilities ALWAYS use the words "when", "whenever", or "at" to describe their trigger conditions. If it doesn't, it is not a triggered ability. Be mindful of the word "if", it does NOT denote a triggered ability, but rather a static ability creating a replacement effect.