The problem is not that we are burning hydrocarbons per se. The problem is rather that these hydrocarbons were extracted from the ground and introduced into the short term carbon cycle. The total amount of carbon rises thereby which leads to shifts like an increasing concentraction in the atmosphere and the oceans. These higher levels of carbondioxide in the atmosphere let less heat escape back into space (the atmosphere is normally somewhat transparent at the affected wavelengths but carbondioxide can absorb at that, trapping additional heat in the atmosphere, see [0]), leading to additional global warming (water vapor also traps heat and and made Earth suitable for life as we know it in first place). Higher levels of carbondioxide in the atmosphere also lead to more carbondioxide being absorbed by the oceans which in turns acidifies the water.
We could extract carbondioxide from air, turn it into hydrocarbons and burn that all day/year/century long but producing it from fossil sources is what makes it so bad.
In a nutshell: You taken carbon dioxide from the air, hydrogen produced with a carbon neutral power source and reverse the process of burning oil. Result: hydrocarbon and oxygen. Costs a fair amount of energy and is comparatively inefficient and costly, but it is carbon neutral since burning that produced hydrocarbon will produce as much CO2 as you used to produce it.
We could extract carbondioxide from air, turn it into hydrocarbons and burn that all day/year/century long but producing it from fossil sources is what makes it so bad.
[0] https://en.wikipedia.org/wiki/Greenhouse_effect#/media/File:...