You didn't take anything apart.
Didn't they get their facts straight? What does this have to do with CO2?
higher CO2 -> higher global temperatures -> decline in plant productivity
Conclusion: higher CO2 isn't necessarily good for plants. Wasn't that your original argument? Are you forgetting what you're even arguing?
How does this relate to CO2? Does CO2 cause droughts? Where do they show that?
higher CO2 -> higher global temperatures -> more drought -> more dead plants
Conclusion: higher CO2 isn't good for plants
Notice there are two ad homiens in one sentence. Really, how can one deny the climate? It's there,.. no need to argue,..Sixth grade logic; good, even a sixth grader understands that CO2 makes plants grow. Why can't the author?
Sixth grade logic: Thinking all plants live in the controlled environment of a greenhouse.
Superior logic: understanding that higher CO2 has global effects that can ultimately lead to a reduction in the well-being of plants.
Conclusion: Higher CO2 in an enclosed environment good for plants. Higher GLOBAL CO2 isn't good for plants.
What does CO2 have to do with Climate Change, extreme weather events, droughts, floods, storms? These type of events have been going on for ages, long before we started emitting CO2,.. Deal with it!
Frequency and intensity. Sorry, but this argument is just idiotic.
I think I've made my point. I don't think I need to go over the rest of your post based on sixth grade logic. 
