https://www.youtube.com/watch?v=zQ3PzYU1N7A
One of the problems cited: the temperature/CO2 graph probably came from an antarctic ice core sample ... and temperature leading/lagging there is different than in non-polar locations.
Second, the climate is a complex feedback system; there isn't one independent variable and everything else is dependent. If something forces any of the variables in the feedback system it can affect the other variables. For instance, say the artificial release of CO2 by humans results in the thawing of the arctic, releasing gigatons of methane, at which point CO2 might no longer be the primary driver. Over geologic time there are different causes for these forcings, but that doesn't mean that the current forcing (human released CO2) isn't the current problem.
He covers all of that and more, much better, in 13 minutes.
[EDIT] I forgot to address "what's even the big issue with changes in global temperatures?"
That is a supremely cavalier attitude. Nobody is saying AGW is going to kill off all life. In the long term life will recover. But in the short term we humans are going to have to deal with the consequences: displacement of millions of people through crop failures and loss of coast, disruption of economic systems, and more civil unrest. The US military is gaming out these scenarios because they believe the science, not because they are pinko tree huggers who hate freedom.