Non Sequitir an/or something else?

"My reading of the current science"  (subjective opinion) " is that the statement that "global climate change to a significant degree is caused by human activity" is not supported by evidence"  (this is just an opinion as well as a false premise) . "I may be wrong,"  (you are) " but most (not all) of those who claim that I am wrong stand on a much shakier ground than me"  (no explanation or evidence given, so its an unsupported claim) .

As stated it is simply an opinion. There are equally qualified climatologists on both sides of this issue. If one relies solely upon the opinion of experts and does not read the underlying basis for the opinion, then you resolve the question by choosing which expert's opinion you want to accept.

My reading of the current science is that the statement that "global climate change to a significant degree is caused by human activity" is not supported by evidence.

Who cares what this person's "reading" is. Are they a climatologist? Are they even a scientist? This is an opinion, and one that might not even matter.

 I may be wrong, but most (not all) of those who claim that I am wrong stand on a much shakier ground than me. 

I can appreciate the humility here at least. It is not clear whether this person is referring to scientific background or evidence here as being on "shakier ground." This, again, is opinion. Saying this is not problematic in itself. They are basically saying that their opinion holds more weight because they have the credentials or evidence to back it up, where the others that simply reject their claim have neither. That is all fine and dandy. However, this only gives their opinion more credibility compared to the opinions of the "others on shakier ground" referred to, NOT compared to the scientific consensus or the actual facts. They did not make this claim, so we shouldn't call them on it.

One last thought about this... the claim "on much shakier ground" can be completely wrong. This person can be a climatologist (have the expertise) and have lots of evidence for their claim, but for some ideological reason, ignoring all the evidence against their claim (i.e., ignoring the convergence of evidence in the field). The person claimed to be "on much shakier ground" could be a layman (non-scientist) who can't recite even one piece of evidence on climate change, but is well aware of the global consensus. It still boils down to an opinion, and has no effect on the truth of the claim.