It is carbon neutral in the way that when you grow algae, unless you are feeding it CO2 produced by burning oil, or something, the carbon will come from the biosphere. When you burn it, you return it. Hence it is carbon neutral (on a relevant timescale, like less than a year.) Incidentally, oil is also "carbon neutral" but only when you consider timescales that are so long so as to be effectively infinite compared to human timescales.

Hold on. Isn't the problem here the fact that the CO2 gets dispersed into the atmosphere? How would this be any different for algae than for petroleum?

And how would algae-produced fuel "return" the CO2 to the biosphere any more than petroleum?

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.

Downvotes for not understanding! Woo!

...grown under the open sun, in ponds. Taking its CO2 from the atmosphere.