Same ones I picked before reading your post. The tarp is protection from the elements, knife is for fire wood, hunting, and just good all around tool. The pot is for water purification and cooking, and the mirror is for signaling for help. It was a toss up between the flare gun and the mirror, but what if the flare got wet?
My way of thinking is I believe most people would panic in such a situation. Panic is what gets people in trouble in most high pressure situations. For peace of mind the water purifier would be a big one for me.
Obviously the knife/cutting device would be essential as a multi purpose tool.
My primary focus would be getting home. I would imagine that the only way one would find themselves stranded on an island would in case of a plane crash or sinking of boat of some kind. These vehicles have built in tracking devices which should lead to a search & rescue of some kind.
A flare gun could save your life if a plane or rescue vessel would approach near your location. The average speed of small plane is around 125-140 mph. I don't know if id wanna chance it with a mirror.
As for a fishing pole...hit or miss based on what maverick says but I'd probably still take my chances.