According to this source, it is claimed that (emphasis is mine)

At Arbikie Distillery in Angus, scientists claim to have developed the world's first "climate positive" gin. By using garden peas instead of wheat, the company has eliminated the need for carbon-intensive fertilizers and can produce animal feed from the leftover material. Taken together, this gives the drink a negative carbon footprint, Arbikie says.

I am having trouble understanding how the act of producing animal feed from the leftovers of a process results in a negative carbon footprint.

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    $\begingroup$ While I definitely welcome any attempt to make a better booze, I too think that this needs further explanation. Especially the part with the peat smoke (terrible CO2 footprint to open up peat), aside from packaging, transportation, infrastructure, ... $\endgroup$ – user20217 Jun 30 at 8:11
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    $\begingroup$ I think they're saying the peas fix nitrogen, and wheat uses fertilizer which has to be produced in a factory, then go through the supply chain to be applied to wheat fields. Does that cancel all of the things @a_donda listed? Your guess is as good as mine. $\endgroup$ – Spencer Jun 30 at 19:16
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    $\begingroup$ However, since this involves economics, which is off-topic, you'll probably want to post this on Sustainable Living SE or Economics Stack Exchange to get a good answer. $\endgroup$ – Spencer Jun 30 at 19:20
  • $\begingroup$ @Spencer What does the carbon cycle have to do with economics? $\endgroup$ – Rodrigo de Azevedo Jun 30 at 19:39
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    $\begingroup$ No, this is (probably) not about the carbon cycle. I think (but don't know because I usually am at the wrong (or right ?) end of the life cycle of the products on question, that in order to judge if the booze is really carbon negative we need to look at the whole process. But I also think they got what they wanted: publicity. Cheers ! :-) $\endgroup$ – user20217 Jun 30 at 20:13

Its only marketing, not a science equation... It's saying that their gin gives back CO$_2$ from other gin which uses fertiliser, and saves a bit of crop space for livestock food. Overall, any crops tend deprive a region of carbon sinks and biodiversity.

Cropland has reduced the worlds total CO$_2$ sinks by 50+ percent, so using 1 crop for 2 things saves CO$_2$ sinks, fertilizer and fossil fuel. Animal stock is intrinsically a climate change accelerator too, especially mammal stocks, which occupy forest space and produce methane and use forest space for hay bales and food crops. Saving surplus foods slightly reduces their impact, its reduces the CO$_2$ budget compared to non surplus feeds.

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  • $\begingroup$ "Saving surplus foods slightly reduces their impact": how (in terms of carbon emitted to the atmosphere)? that is the question! $\endgroup$ – onurcanbkts Jul 1 at 4:26
  • $\begingroup$ Because cropland has reduced the wotlds total CO2 sinks by 50+ percent, so using 1 crop for 2 things saves co2 sinks, fertilizer and fossil fuel. $\endgroup$ – aliential Jul 1 at 7:40

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