This is a delicate topic that mixes questions of halacha with hashkafa. The answer will also depend on the type of women's prayer group being discussed (e.g., regular service addressed below vs. one-off Simchat Torah or bat mitsva ceremony). I will try here to surface some of the arguments and refer the interested reader to additional sources.
In a nutshell very prominent Modern Orthodox poskim were opposed to women prayer groups for full services although some others allowed them in limited settings such as Megilla readings. One of the reasons is to allow women to participate in regular synagogue services where they also belong.
R Gil Student summarizes here the position of R Yosef Dov Soloveitchik. There is debate whether R Soloveitchik's opposition was matter of strict halakha, of halakhic values or of public policy but it came from multiple directions: deviation from customs, beginning of larger-scale reform, improper motivation, inauthentic practice, distortion of Torah, non-halakhic agendas, heterodox practices and community divisiveness.
In a similar survey of R Herschel Schachter's position (here), R Gil Student lists another set of drivers for his opposition to what he calls a "improper and even dangerous innovation", e.g., incomplete mitzvot (i.e., missing minyan and kaddish, kedushah, barekhu, repetition of the amidah and an official reading of the Torah), breaking from normative halakhah, impure motivations, lack of established custom, improper synagogue customs, imitating non-Jews.
R Shlomo Goren did write a responsa permitting women prayer groups (see here for a summary which contradicts his arguments) but retracted it at the end of his life.
As noted in the introduction, there are more restricted settings where women prayer groups might be appropriate and halakhically permitted (e.g., Rs Frimer mention R Moshe Feinstein permitting a Megilla reading (see also here from R Michael Broyde), or the London Beit Din permitting Kabalat Shabbat, Hallel or a Torah reading without blessings, as long as this is done for pure motives).