The BBC is reporting that Meat and Livestock Australia (MLA) is reporting that "greenhouse gas emissions from the industry have fallen by almost 60% since 2005". This seems to be from the MLA State of the Industry Report 2019 which says:
a 57.6% reduction in greenhouse gas (GHG) emissions across the beef, sheepmeat and goatmeat production sectors since the CN30 baseline year of 2005. The data was compiled by CSIRO from the Australian National Greenhouse Gas Inventory and shows the red meat industry reduced GHG emissions from 129.3 million tonnes of C02 equivalent (Mt C02-e) in 2005 to 54.8 million Mt C02-e in 2016.
Looking at the National Greenhouse Gas Inventory they have a spreadsheet of emmissions by sector from 1990 to 2019, and the relevant numbers of Greenhouse gas emissions (kt CO2-e) for 2005 and 2016 are:
|A. Enteric fermentation||64,251||55,979||13%|
|B. Manure management||7,644||7,186||6%|
|C. Rice cultivation||230||124||46%|
|D. Agricultural soils||11,515||11,617||-1%|
|F. Field burning of agricultural residues||353||300||15%|
|H. Urea application||887||1,510||-70%|
I cannot see how you could get from these numbers to a 57.6% reduction. I think the main emission of red meat production is enteric methane, which accounts for 72-74% of all agricultural GHG. This has a drop of only 13%.
Is there any way to read these numbers to get a figure of 57.6% reduction?