Yes, Humans Can Have An Effect On Climate
We already know that we've increased the CO2 content of the atmosphere by 20%. If human activities are too small to affect the Earth, how do you explain that?
The total CO2 content of the atmosphere is 2800 billion tons of CO2. Humans are burning enough coal, oil, and natural gas to put an extra 26 billion tons of CO2 into the atmosphere each year. At this rate atmospheric CO2 content will double in 108 years. You don't think that's going to have an effect?
Water vapor accounts for 66% to 85% of the greenhouse effect, whike CO2 accounts for 9% to 26%.
So, yes, human activities CAN and we DO have a significant effect on Earth's atmosphere. The greenhouse effect increases the Earth's surface temperature by about 33C over what it would be without those gasses. Doubling the CO2 content will add another 5C or so to that.
During the 60s humans started burning a lot of high-sulfur coal, resulting in sulphate aerosols that blocked out the sunlight so we had a cooling spell until laws were passed to limit sulfur emmissions. Of course humans can have an effect on the Earth's climate.
Sure, there are natural cycles, but just because there are natural cycles doesn't mean there isn't a man-made effect on top of them.