The phrase "a point of emphasizing" is not correct in standard written English.
It seems to be an attempt to convey the idea of highlighting or stressing something, but it is awkwardly phrased.
Example: "In this report, I want to make a point of emphasizing the importance of teamwork in achieving our goals."
Alternatives: "a point of emphasis" or "a point to highlight".
In its work here, officials of the United Nations mission have made a point of emphasizing the organization's impartiality.
And the mayor has always made a point of emphasizing that discovering human remains was a top priority even as the bulldozers moved in.
Meanwhile, key officials at the central bank are making a point of emphasizing the bank's willingness to raise rates at the slightest hint of higher inflation.
Our desserts are also different, and we make a point of emphasizing them instead of them being an afterthought, like they can be at Indian restaurants.
Secretary of State John Kerry made a point of emphasizing that distinction in his criticism of China's new zone on Saturday.
When we spoke, he made a point of emphasizing the influence of icons of the right, like the libertarian economist Friedrich von Hayek and the originalist legal scholars.
Mr. Hill makes a major point of emphasizing the extent to which his mother, Tabitha King, has influenced his work, no matter how eagerly others connect his writing with his father's.
Google has made a public relations point of emphasizing its free-to-employees cafeteria, whose original chef had worked for the Grateful Dead.
Objective To examine the effects of a point-of-purchase (POP) intervention emphasizing various properties of healthful food items on college students' snack purchases.
The work with local people in the villages emphasized that a point-of-use water treatment was most important for the treatment concept.
There, he repeatedly made a point of downplaying his credentials, emphasizing that Congress's role on foreign policy is secondary to the president's, and joking that he is usually more comfortable in his "cocoon" at the Heritage Foundation and the American Enterprise Institute.
