[CTcard]

Two reasons.  One is that they said so.  From their FAQ:

Stanford’s more than 850 varsity student-athletes today represent 12% of our undergraduate population, a far higher percentage than exists at nearly all of our peer institutions.

After the cuts, that percentage will be 9%.

Well, I continue to agree with your logic, though that statement isn't quite saying so.

It also isn't quite true, depending I guess on exactly what they consider their peer institutions and some quibbles about level of varsity athlete.

Princeton currently claims "about 18 percent of undergraduates participate in varsity sports, spanning 37 varsity men’s and women’s teams."
Yale, at least in spring 2017, claimed "33 varsity teams and 833 student athletes" which would be about 833/6092 = 13.7%.
Harvard: "Nearly 1200 students — roughly 20 percent of the student body — participate in one of Harvard's 42 varsity teams, the most offered among NCAA Division I colleges."
Columbia: "Columbia University in the City of New York competes in 27 sports and has a total of 844 student athletes" or about 844/9000 = 9.4%
Penn: "University of Pennsylvania competes in 28 sports and has a total of 1033 student athletes" or about 10%.
Cornell: I see conflicting numbers, somewhere between 30 and 37 varsity sports, and at least one site lists 1351 student athletes, or about 9% of undergrads.
Dartmouth: Don't see a number, but see an article in 2019 claiming "over a fifth of the current student body is comprised of varsity athletes."
Brown: "Brown University competes in 33 sports and has a total of 1026 student athletes" or about 10% of undergrads.

Of course there is a similar reconsideration of athletics going on across the Ivy League, with Dartmouth and Brown cutting or moving several sports to club status. Dartmouth appears to have explicitly linked the cuts to the balance of its student body.

Hanlon wrote that "with 35 varsity teams and the smallest enrollment within the Ivy League, athletic recruitment at Dartmouth has begun to impact our ability to achieve the right balance between applicants who are accomplished in athletics and applicants who excel in other pursuits. To achieve greater flexibility in shaping the incoming class, I asked Harry to reduce the number of recruited athletes in each entering class by 10%."

https://news.dartmouth.edu/news/2020/07/dartmouth-announces-changes-varsity-athletics-program 

[CTcard]

Two reasons.  One is that they said so.  From their FAQ:

Stanford’s more than 850 varsity student-athletes today represent 12% of our undergraduate population, a far higher percentage than exists at nearly all of our peer institutions.

After the cuts, that percentage will be 9%.

Well, I continue to agree with your logic, though that statement isn't quite saying so.

It also isn't quite true, depending I guess on exactly what they consider their peer institutions and some quibbles about level of varsity athlete.

Princeton currently claims "about 18 percent of undergraduates participate in varsity sports, spanning 37 varsity men’s and women’s teams."
Yale, at least in spring 2017, claimed "33 varsity teams and 833 student athletes" which would be about 833/6092 = 13.7%.
Harvard: "Nearly 1200 students — roughly 20 percent of the student body — participate in one of Harvard's 42 varsity teams, the most offered among NCAA Division I colleges."
Columbia: "Columbia University in the City of New York competes in 27 sports and has a total of 844 student athletes" or about 844/9000 = 9.4%
Penn: "University of Pennsylvania competes in 28 sports and has a total of 1033 student athletes" or about 10%.
Cornell: I see conflicting numbers, somewhere between 30 and 37 varsity sports, and at least one site lists 1351 student athletes, or about 9% of undergrads.
Dartmouth: Don't see a number, but see an article in 2019 claiming "over a fifth of the current student body is comprised of varsity athletes."
Brown: "Brown University competes in 33 sports and has a total of 1026 student athletes" or about 10% of undergrads.

Of course there is a similar reconsideration of athletics going on across the Ivy League, with Dartmouth and Brown cutting or moving several sports to club status. Dartmouth appears to have explicitly linked the cuts to the balance of its student body.

Hanlon wrote that "with 35 varsity teams and the smallest enrollment within the Ivy League, athletic recruitment at Dartmouth has begun to impact our ability to achieve the right balance between applicants who are accomplished in athletics and applicants who excel in other pursuits. To achieve greater flexibility in shaping the incoming class, I asked Harry to reduce the number of recruited athletes in each entering class by 10%."

https://news.dartmouth.edu/news/2020/07/dartmouth-announces-changes-varsity-athletics-program