the yeshiva in volozhin was closed due to the maskilim influencing the russian government to insist on rules designed to force its closure. As explained by the torah temmia, a talmid of the yeshiva and a nephew of the netziv, the issue was not secular studeies per se . In fact the netziv had agreed to teach math and russian language to the students..
As satated at page 203, in the book My uncle the nitziv, the russians requied general studies from 9 to 3 in the afternoon, no talmud studies at night, no learning in total more than ten hrs a day including 6 hrs of secular, and all teachers had to have an education degree.
obviously this was not a simple issue of secular studeis to help earn a parnosa. In fact during the winter months no time at all wpuld remain for stdy of talmud according to the torah temmia, who also was the son of the aruch hashulchan.
the entire plan of the maskilim was to close the yeshiva be cause it presented a success story and such a strong counterpoint to thier ideals. The torh Temmia himself wrote a boook on banking while at volozhin and states that”in volozhin torah and derech eretz walked hand in hand.
I do not wan TO opine as to the underlying issue,but only want to set the record correctly.