Very few people make the argument that climate change isn't happening. The "anti" argument is that it's not due to mankind's activity, but rather a natural cycle, and has changed in the past, will change in the future. The anti position also questions how much the change is happening -- whether it's a 10-20 year spike vs. a 100 year increase, etc. (and, even if you believe in anthropogenic, it's quite reasonable to think there are natural climate cycles going on as well -- just that mankind's involvement is in addition to this and might push outside the normal range)

Humans also almost assuredly can change climate, if they want. It's a lot easier to cool vs. warm -- set off a bunch of nuclear weapons (easy, produces nuclear winter, although maybe less so than fearmongered); or, be sane, and put a bunch of sulfur dioxide into the atmosphere to reflect more sunlight and thus cool the Earth.

I personally think it's probably prudent to try to reduce CO2 emissions, but not drastically. The costs (financial and quality of life) of massive reductions in CO2 now are far higher than the costs to remediate with SO2 or other methods, at least until there's more precise data, the costs of reducing CO2 emissions are reduced, etc. We could probably drop them by a good amount in the developed world, but doing so in China/India/etc. would mean an unreasonable restriction on quality of life for billions of people.