Here is a link to Oxfam's methodology[1].
First, they only track emissions that they can directly tie with consumption. The statement "fifty percent of the world’s carbon emissions are produced by the world’s richest 10%" is not supported by the study because it makes no attempt to track all of the world's carbon emissions.
Second, they assume that income == consumption == carbon emissions, which is a very bad assumption. The world's richest people do not spend their entire income every year, so using that as the basis for consumption is inaccurate. Also, assuming that every dollar spent, no matter where or by whom, has the exact same emissions associated with it is incorrect. Wealthy people are the people who can afford to put solar panels on their roofs and buy new electric cars, but by this study they are penalized for such consumption.
In general, I find that oxfam optimizes their studies for the headlines. When you dig into it, there are so many qualifiers and assumptions made that it seems clear the study was authored with an specific outcome in mind.
"The top 10% earn 5x more money than average" is not as outrageous a headline as we are used to seeing. But by multiplying by a carbon emission factor of 1, they get to write "Top 10% emits half of world's carbon", which generates way more clicks.
[1]https://oxfamilibrary.openrepository.com/bitstream/handle/10...