David- no worries, just repeating what I've read for your benefit because it seems you missed that detail. I was surprised by the annual sawtooth when I first saw the data, many years ago- but not nearly as unpleasantly surprised as I was to see the overall, rather unmistakeable trend in the data.
Yes, the biological flows are large. The concentration in the atmosphere is like the level in a tank. The flow in or out doesn't matter really- all that matters is the size of the tank and the difference between the two total flows in and out. Regrettably, the size of the tank is finite, and the mass of fossil carbon stored over a billion years or more is enormous, so if we keep going the way we're going, the level will continue to rise. The "tank" in this case is really a whole series of tanks, each with its own input and output flows and its own accumulation positive or negative- the atmosphere itself, dissolved gases in the oceans, and the various natural carbon "sinks" and sources both geological and biological. The rates into and out of those various secondary tanks can vary greatly also, and each has its own equilibria. Some of those individual rates have time constants on the order of days, others on the order of centuries, and others on the order of hundreds of thousands of years, so it's possible to tease out which ones are going to respond quickly enough to be of relevance to the atmospheric concentration on the human timescale.
It's a very complex system, but what we see is that inexorable increasing trend, which from what I've read, happens to coincide in timing, isotopic composition and rough magnitude to what would be expected from our historical fossil carbon emissions. While correlation doesn't guarantee causation, it's a stretch to imagine an alternative explanation that is going to fit the data better.
As to mixing effects in the atmosphere due to winds etc., if it were a significant effect I would expect the data to look quite a bit more variable than it is.
One thing the data makes quite obvious is that there's no way that volcanic eruptions are sufficient to explain the increase or would overwhelm human-generated emissions. I've seen that claim made here and elsewhere and have swatted it down as specious, because it clearly is. Mt. St Helens, Pinatubo etc. are barely blips on the measurement.