This is common sense, but it is also climate physics.
The amount of carbon in our atmosphere is rising for the same reason that a tub left to fill will overflow if the drain has plugged: carbon is being added to the atmosphere faster than the Earth's surface can reabsorb it.
Primarily through our burning of fuels (but also through our cutting down of forests), we are in fact adding carbon to the atmosphere twice as fast as the Earth can remove it. True, our 10 gigatonnes/year in carbon emissions is small compared to Nature's own contributions, but it is enough to push the carbon cycle out of balance. Specifically, it is twice the 5 gigatonne/year rate at which the Earth is currently able to reabsorb that extra carbon (in the form of plants, algae, and an acidifying ocean), and, as a consequence, the level of carbon — primarily in the form of carbon dioxide — in the atmosphere continues to rise.
In my nearly 60 year lifetime, carbon dioxide levels have risen 30% (from 315 ppm to 410 ppm). This is our doing: carbon dioxide levels in the atmosphere are rising because of the added carbon dioxide we are putting into the atmosphere through the burning of fuels. What's more, the yearly rate of increase has doubled over these same 60 years. We aren't just failing to patch the holes in our atmospheric life boat. We're actively punching more holes in the hull (and the boat's captains have been encouraging us on)!
So why are rising levels of carbon dioxide are of concern? One important reason is that the carbon imbalance in the atmosphere is causing an energy imbalance at the Earth's surface. The Earth's surface is being heated faster than it can cool, and as a result, decade after decade, global average surface temperatures continue to rise, albeit with occasional fits and starts rather than a simply smoothly rising curve. Over time, however, the trend becomes clear, and it is no surprise that "seventeen of the 18 warmest years in the 136-year record all have occurred since 2001."
Why is this warming not a surprise? Because the basic mechanism by which rising carbon dioxide levels lead to global warming has been understood for more than a century. Current questions within climate physics concern whether a particular feedback mechanism will accelerate or slow down the rate of warming, and if so, by how much. The question is not whether warming will occur at all.
We have known since the work of Fourier in 1824 that (1) the Earth's surface temperature is determined by a balance between the rate at which energy is received and the rate at which energy is lost, (2) the Earth's surface absorbs energy arriving from the sun as visible light and loses energy by emitting infrared light (which we can feel upon our skin but is invisible to our eyes), and (3) that because the atmosphere is transparent to visible light but absorbs (and then radiates back to the surface) infrared light, the atmosphere acts as a blanket to keep the surface warmer than it would have been.
We have known since the work of Tyndall in the 1860's that the atmospheric absorption and re-radiation of infrared light (which in turn results in surface warming) is due to only a few trace (rare) "greenhouse" gases such as water vapor, carbon dioxide, and methane. Most of the atmosphere — nitrogen and oxygen, for example — has no effect.
We have known since the pioneering work of Arrhenius in 1896 (1) how to use the principle of energy balance to physically determine the changes in surface and atmospheric temperatures that result from doubling the amount of carbon dioxide in the atmosphere (2) how losses in ice coverage resulting from surface warming would intensify warming near the poles (due a process known as the ice-albedo feedback mechanism) and (3) how the increase in atmospheric water vapor resulting from surface warming would further increase the warming effect of carbon dioxide.
By 1970, we knew from a decade of measurements by Charles Keeling that that the carbon cycle was out of balance and atmospheric carbon dioxide levels were rising due to the burning of carbon-based fuels including coal, oil, and gas.
By 1974 Syukuro Manabe and Richard T. Wetherald had developed the first modern computerized model of the atmosphere. They found that as a result the water-vapor feedback mechanism first introduced by Arrhenius, further warming will occur even if carbon dioxide levels stopped rising.
By 1984 James Hansen and colleagues at NASA had established through computer models that the slowness of the ocean to fully warm causes a delay of up to a century between the addition of carbon dioxide to the atmosphere and when the full effects of global warming occur, just like the delay in warming of the ocean compared to the sand on a beach on a sunny day. That warming, however, is already "in the pipeline" and will occur even if the carbon cycle is later brought into balance.
Yesterday (23 June 2018) marks the 30th anniversary of James Hansen's 1988 testimony alerting Congress to the coming danger of global warming due to rising levels of carbon dioxide. His predictions have proven correct.
Now, like young beachgoers beginning to worry that a rising tide will wash away their sandcastles, the question has become not Earth's surface temperature will continue to rise, but by how much. Strangely, the answer depends on us.
The longer we continue to burn in excess of what the carbon cycle can reabsorb, the more Earth's surface will ultimately warm even if we stop all burning fossil fuels altogether. In a 2013 article in Science entitled "The Closing Door of Climate Targets," a prominent climate scientist estimated that staying below the Paris Climate accord target of 2 °C (3.6 °F) of warming will require across the board emission reductions of roughly 3 %/year every year if we start in 2020, 5%/year if we start in 2030, and 10%/year if we start in 2035. 2° C becomes impossible in 2045. 1.5° C becomes impossible in 2030. If the estimate is correct, it is already impossible to keep warming below 1 °C.
These estimates, of course, have some uncertainty with regard to specific dates. What is not uncertain is the conclusion: "even well-intentioned and effective international efforts to limit climate change must face the hard physical reality that certain temperature targets can no longer be achieved if too much carbon has already been emitted to the atmosphere."
On the face of it, 2 °C of warming might seem little concern, particularly if you are looking forward to a day at the beach.
But global warming doesn't just lead to rising temperatures. It also leads to a more unstable climate, and ultimately, past a tipping point, a runaway climate . Knowing that humans have been around for some 200,000 years — including a few ice ages — some of us are not yet worried. Civilization, however, has only been around for at best the 20,000 years. That's in part because until then, the climate wasn't stable enough for farming to succeed and for cities to grow. Without a stable climate, will there be a time to reap and a time to sow? The planet is now already as warm as it has ever been in all of civilization.
In the end, we are all in the same boat, and if we seek to avoid a tipping point, we have to patch the holes. 
If we want carbon dioxide levels to stop rising, we have cut emissions at our smokestacks, tailpipes, and chimneys by more than half. But if we want to lower CO2 levels from today's already high levels and do it quickly enough to meet commonly agreed upon climate targets, we need even larger reductions in emissions.
The Paris Climate Accord target of 80% reduction in emissions by 2050 comes from an effort to keep the total increase in average planetary temperature to no more than 2 °C (3.6 °F). Some climate scientists argue that based on the paleoclimate record, 2° C is already historically unsafe, and that CO2 levels need to be brought down to 350 parts per million soon enough to limit warming to 1 to 1.5°C. Their arguments are the basis of 350.org. Doing that will require reducing emissions to zero, and doing so at a rate of at least 5%/year, starting now.
We are nowhere close.
 Why? Because the infrared energy radiated back to the surface combines with the energy arriving by sunlight to increase the total amount of energy/second arriving at the surface. So the surface warms. We have known since the work of Stefan and Boltzmann in the 1880's that the rate at which the Earth will radiate infrared energy will increase as it warms, and we have known since Planck's quantum theory of thermal radiation in 1900 how that happens. If nothing else changes, the surface ultimately comes to a new (but warmer) steady-state temperature. Problem is, the Earth takes a long time to fully warm. The other problem? We continue to change the atmosphere!
Why does this matter? Because even though these "greenhouse" gases make up such a small amount of the atmosphere, they have a huge effect on the planetary temperature. And the smaller the amount initially in the atmosphere, the bigger the effect of adding of adding even a small amount more. “Before Tyndall,” writes renowned climate physicist Raymond Pierrehumbert, “no one had any reason to connect the Industrial Revolution with climate change.” After Tyndall, it was clear that the burning of coal could indeed change the temperature of the planet, if the carbon cycle were thrown out of balance.
 But the last time our planet was that warm (during the slow cooling that followed the collision of India with Eurasia and the formation of the Himalayas), there were no ice sheets at all in the northern hemisphere, the Antarctic ice sheets had only just formed, and sea levels were some 20 meters (65 feet) higher than today. That won't happen right away. There's hysteresis in the climate system.It is greater than what has been predicted to occur in this century. But it is where the paleoclimate record says the planet is headed, given enough time. A rising tide might lift all boats, but our ports would be under water!
 Of course, the leaky row boat is just an analogy. Our planetary boat differs from a row boat in three important details: (1) we have no shore to swim to if our boat sinks, (2) we are actively punching new holes in the hull, and (3) we have no other boat. Time to patch the holes!