"personal argument" is correct and usable in written English.
You can use it to refer to a kind of argument based on an individual's beliefs, values, or experiences. For example: "My personal argument is that we should focus on sustainable materials when designing our products."
The site was already established as a favorite spot for duelists by the time Burr and Hamilton arrived to settle a political and personal argument that had been going on for years.
WASHINGTON -- Raising the minimum wage makes sense to anybody who has ever worked an hourly job, President Obama said in a freewheeling and highly personal argument he debuted on Wednesday.
But Graham, who served as governor of Florida before going to the Senate, would not make the same personal argument that Hart did when it came to Jeb Bush.
The shooting did not appear to be connected to the anti-Trump demonstrations but instead stemmed from a personal argument, said Robert Merner, assistant chief of the Seattle Police Department.
Rather, they are rooted in a mixture of personal arguments and cultural misunderstandings that can flare fatally among heavily armed young men.
Beyond the parliamentary maneuvering, Vietnam War veterans dominated the day's debate in both chambers, rising to make passionate and deeply personal arguments both for and against invasion.
Halsted and her Soviet counterpart Vadik Chapayev (Michael Mendelson), forced to share the cramped, frigid observatory atop the research station, find that arguments over science and politics quickly turn personal — and that personal arguments spill into science and politics.
In November, the opposition leveled allegations of corruption stemming from Mr. Gillard's past work as a young labor lawyer, leading to vitriolic and deeply personal arguments on the floor of Parliament.
José Mourinho has said he will not get into personal arguments with Pep Guardiola next season when they are in charge of Manchester United and Manchester City respectively as it would mean "someone else" winning the title.
As a result, a mutual exchange of experts' personal arguments for the ranking took place during the workshop sessions.
Support from science teachers is essential, as it has been found that many students need appropriate guidance and scaffolds to conduct high-order reasoning and develop sounder arguments (e.g., reflection or evaluation of personal arguments) regarding SSI (Naylor et al. 2001; Simon et al. 2006; Zohar & Nemet, 2002).
