The atmosphere is part of the biosphere. Plants growing take their CO2 out of the atmosphere. Algae take it out of the oceans, but CO2 in the oceans is in equil

The atmosphere is part of the biosphere. Plants growing take their CO2 out of the atmosphere. Algae take it out of the oceans, but CO2 in the oceans is in equilibrium with the atmosphere. (True, the timescale for that is a bit longer, but still pretty short for surface waters where photosynthesizing algae live.) The difference is not where the CO2 end up, it's where it came from. The carbon in any algae you find today was taken out of the atmosphere within the past ~year. The carbon in petroleum was taken out 50 million years ago. It's that difference in time scale, or equivalently the size of the reservoir, that determines whether something counts as "carbon neutral" or not. The amount of carbon in algae is very small compared to the total carbon budget of the biosphere. The amount in petroleum is not.