And if you look at it in 100 year increments then anyone who died less than 50 years ago would be alive
That is fundamentally not true. All of my grandparents died in the last 50 years, and none of them were alive 100 years ago. Whether or not, I can convince you that any of the rest of what you said wasn't logically valid, please, PLEASE, acknowledge that you got this one wrong.
To your larger point about implying that time scales of human lives are somehow significant and as such picking them is not arbitrary. What does the human life span have to do with it. According to wikipedia we know about 15 trees that are over 2000 years old (we don't know the ages of all the trees) And there are some whole forests that are same tree that we think are 10s of thousands of years old, and it take our intervention to extend a fruit fly life span up to 3 months. Why is our lifespan somehow special when studying the climate? Why are humans the organism with the magic life span?
As to your boiling water analogy, Imagine that you had a pot of boiling or near boiling water in that state for extremely long period of time (years) then something disturbed it and it's temperature dropped to 30 degrees, before starting to climb back up, and then we found it when it was back up to 40. We'd wonder why the water was so cool, even though it was on it's way back to normal. But if the whole change in temperature happened because an external factor came into play and then was removed, and you are only looking at the period where the temperature was back on the rise, and are looking for a why, you're not going to find it because it's not there. That goes to you "only happened in the last hundred or so years", comment as well. By only looking at the period over which something is happening you can't isolate any other unusual activity as the cause if you don't have the context required to rule out all the usual activity. This is why scientific experiments require repetition and controls. Since that's not available all possible context is required.
But again I'm not saying what time period is relevant. I'm trying to make the distinction that arbitrary timescale choices aren't valid for refuting the validity for choosing other arbitrary time slices.
Give a man a fish, and you feed him for a day. Teach a man to fish, and he'll invite himself over for dinner. - Calvin Keegan