I don't know who this Rabbi is or how influential the school he works at is. I've never heard if either. It's not uncommon for Rabbis to be against women joining the army, although usually the reason given is that of the other Rabbi in the article.
I did however find
this article which includes a part that Hadashot unfortunately didn't deem important enough to include.
בתגובה לפרסום הדברים, שיגר הרב קלנר הודעת התנצלות. "אני מצטער שיצא ממני דבר כזה, לפעמים אדם נכשל", מסר. "היום לא הייתי אומר את הדברים. הכול באחריותי, חבריי למכינה מתנגדים לסגנון ולתוכן".
מהמכינה בעלי נמסר: "במוסדות בני דוד מלמדים מעל 40 רבנים שמעבירים עשרות שיעורים מדי שבוע בהם נשמר חופש ביטוי מלא גם לרבנים וגם לתלמידים איש איש ותפיסתו. הדבר נכון בעיקר במקרים מסוג זה בהם דברי הרב אינם משקפים את רוח בני דוד וראשי המכינה חלוקים עליהם".
In reaction to the publication of these things, Rabbi Kelner sent a letter of apology. "I apologize that such a thing came out of me. Sometimes a person fails," he sent. "Today, I would not say these things. Everything is my responsibility, my friends at the preperatory school oppose the style and content [of my words]."
The preparatory school sent, "At Eli institutions there are over 40 Rabbis giving tens of lectures ever week. In them, full freedom of expression is preserved for both Rabbis and students according to their own perceptions. This is especially true in these types of cases where the words of the Rabbi do not reflect the spirit of B'nei David (the insitution) and the heads of the preparatory school disagree with them.
Edit: Also I think portraying sexism as a problem of religion is disingenious as it conveys that idea that secular people can't be or never are sexist.