I assume he used "instinctively" precisely because he doesn't know exactly why. Perhaps, "intuitively" might have been a better choice of word here.

Just to give my view: Because it's an engineering approach. We don't have to completely understand a highly complex system before we can make some fixes. Intervening before it breaks frees us from the work of repairing what we can't manage. This resonated with me the first time I read about it.

Hmmm, perhaps "instinctively gravitated toward the opinion that Aubrey de Grey was correct". That's more accurate; my "knowledge" does not, of course, imply proof of correctness.

death is bad

That doesn't imply anything about the most effective way to increase longevity.

I think you're reading too much into the words "right approach." In this case, "right approach" (I think) means something like "understanding that death is bad and trying to fight it."