The cartoon seems to originate from Resources Spent on Consumption of Animals (citing to a video from Bite Size Vegan) which gives slightly more detail:
1 lb of beef = 55 square feet of forest (45-55 trees)
One year using NO paper saves 8.51 trees vs. foregoing 1 lb of beef, which saves 45-55 trees
One year eating no beef saves 3,432 trees
So the assumption is that cattle are grazing upon land that would be forested without human intervention.
The most obvious problem with this analysis is that there are much fewer than 45 trees per 55 square feet.
One acre is 43560 square feet.
According to Tufts University Office of Sustainability:
Tree density varies, and we used an average of 700 trees per acre (this number was taken from DOE’s "Sector-Specific Issues and Reporting Methodologies Supporting the General Guidelines for the Voluntary Reporting of Greenhouse Gases under Sections 1605(b) of the Energy Policy Act of 1992")
(Even 700 trees per acre is a very high estimate. See the recent Nature article Mapping tree density at a global scale, Fig. 3, that shows that depending upon the type of ecosystem tree density varies from 200 to 1000 per hectare, or 80 to 400 per acre)
700 trees per 43560 square feet is 1 tree per 62 square feet.
So even assuming that all cattle graze on land which was previously forested (rather than the Great Plains of North America which were naturally grasslands with millions of bison), the cartoon is off by a huge factor on the number of trees per acre (trees per pound of beef).
The next major problem with the cartoon (as PhillS is commenting) is more subtle, but also very severe. The time for trees to grow to make paper is 25-40 years. So, when comparing to using trees for paper, it doesn't make sense to count the acreage (square footage) as if 700 trees could grow on one acre in one year.
For comparison to reality, taking the United States for example, according to the United States Forest Service:
In 1630, the estimated area of U.S. forest land was
1,023 million acres or about 46 percent of the total
land area. Since 1630, about 256 million acres of forest
land have been converted to other uses—mainly
So if everyone in the United States just killed themselves, and let the full 256 million acres of forest lost regrow, this would be 256 million acres per 323 million people or 0.79 acres per person. With 700 trees per acre, 555 would be saved per person. Not 555 trees per year, but 555 trees per lifetime of a tree.
Furthermore, according to the Nature article cited above, globally there is a:
gross loss of approximately 15.3 billion trees on an annual basis
This is about 2 trees per person per year. So stopping all deforestation for all reasons (not just beef, not just all meat, but all human activity) would save 2 trees per person per year.